@article{AlhaddadFoerstnerGrothetal., author = {Alhaddad, Samer and F{\"o}rstner, Jens and Groth, Stefan and Gr{\"u}newald, Daniel and Grynko, Yevgen and Hannig, Frank and Kenter, Tobias and Pfreundt, F.J. and Plessl, Christian and Schotte, Merlind and Steinke, Thomas and Teich, J. and Weiser, Martin and Wende, Florian}, title = {The HighPerMeshes Framework for Numerical Algorithms on Unstructured Grids}, series = {Concurrency and Computation: Practice and Experience}, volume = {34}, journal = {Concurrency and Computation: Practice and Experience}, number = {14}, doi = {10.1002/cpe.6616}, abstract = {Solving PDEs on unstructured grids is a cornerstone of engineering and scientific computing. Heterogeneous parallel platforms, including CPUs, GPUs, and FPGAs, enable energy-efficient and computationally demanding simulations. In this article, we introduce the HPM C++-embedded DSL that bridges the abstraction gap between the mathematical formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different programming models on the other hand. Thus, the HPM DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HPM DSL, and demonstrate its usage with three examples. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters, is presented. A code generator and a matching back end allow the acceleration of HPM code with GPUs. Finally, the achievable performance and scalability are demonstrated for different example problems.}, language = {en} } @article{AlhaddadFoerstnerGrothetal., author = {Alhaddad, Samer and F{\"o}rstner, Jens and Groth, Stefan and Gr{\"u}newald, Daniel and Grynko, Yevgen and Hannig, Frank and Kenter, Tobias and Pfreundt, Franz-Josef and Plessl, Christian and Schotte, Merlind and Steinke, Thomas and Teich, J{\"u}rgen and Weiser, Martin and Wende, Florian}, title = {HighPerMeshes - A Domain-Specific Language for Numerical Algorithms on Unstructured Grids}, series = {Euro-Par 2020: Parallel Processing Workshops.}, journal = {Euro-Par 2020: Parallel Processing Workshops.}, publisher = {Springer}, doi = {10.1007/978-3-030-71593-9_15}, pages = {185 -- 196}, abstract = {Solving partial differential equations on unstructured grids is a cornerstone of engineering and scientific computing. Nowadays, heterogeneous parallel platforms with CPUs, GPUs, and FPGAs enable energy-efficient and computationally demanding simulations. We developed the HighPerMeshes C++-embedded Domain-Specific Language (DSL) for bridging the abstraction gap between the mathematical and algorithmic formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different parallel programming and runtime models on the other hand. Thus, the HighPerMeshes DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HighPer-Meshes DSL, and demonstrate its usage with three examples, a Poisson and monodomain problem, respectively, solved by the continuous finite element method, and the discontinuous Galerkin method for Maxwell's equation. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters is presented. Finally, the achievable performance and scalability are demonstrated for a typical example problem on a multi-core CPU cluster.}, language = {en} } @inproceedings{AndresArconesWeiserKoutsourelakisetal., author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins}, series = {5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering}, booktitle = {5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering}, pages = {1 -- 15}, abstract = {In recent years, the use of simulation-based digital twins for monitoring and assessment of complex mechanical systems has greatly expanded. Their potential to increase the information obtained from limited data makes them an invaluable tool for a broad range of real-world applications. Nonetheless, there usually exists a discrepancy between the predicted response and the measurements of the system once built. One of the main contributors to this difference in addition to miscalibrated model parameters is the model error. Quantifying this socalled model bias (as well as proper values for the model parameters) is critical for the reliable performance of digital twins. Model bias identification is ultimately an inverse problem where information from measurements is used to update the original model. Bayesian formulations can tackle this task. Including the model bias as a parameter to be inferred enables the use of a Bayesian framework to obtain a probability distribution that represents the uncertainty between the measurements and the model. Simultaneously, this procedure can be combined with a classic parameter updating scheme to account for the trainable parameters in the original model. This study evaluates the effectiveness of different model bias identification approaches based on Bayesian inference methods. This includes more classical approaches such as direct parameter estimation using MCMC in a Bayesian setup, as well as more recent proposals such as stat-FEM or orthogonal Gaussian Processes. Their potential use in digital twins, generalization capabilities, and computational cost is extensively analyzed.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal., author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {A Bayesian Framework for Simulation-based Digital Twins of Bridges}, series = {EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability}, volume = {6}, journal = {EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability}, number = {5}, doi = {10.1002/cepa.2177}, pages = {734 -- 740}, abstract = {Simulation-based digital twins have emerged as a powerful tool for evaluating the mechanical response of bridges. As virtual representations of physical systems, digital twins can provide a wealth of information that complements traditional inspection and monitoring data. By incorporating virtual sensors and predictive maintenance strategies, they have the potential to improve our understanding of the behavior and performance of bridges over time. However, as bridges age and undergo regular loading and extreme events, their structural characteristics change, often differing from the predictions of their initial design. Digital twins must be continuously adapted to reflect these changes. In this article, we present a Bayesian framework for updating simulation-based digital twins in the context of bridges. Our approach integrates information from measurements to account for inaccuracies in the simulation model and quantify uncertainties. Through its implementation and assessment, this work demonstrates the potential for digital twins to provide a reliable and up-to-date representation of bridge behavior, helping to inform decision-making for maintenance and management.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal., author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {Model bias identification for Bayesian calibration of stochastic digital twins of bridges}, abstract = {Simulation-based digital twins must provide accurate, robust and reliable digital representations of their physical counterparts. Quantifying the uncertainty in their predictions plays, therefore, a key role in making better-informed decisions that impact the actual system. The update of the simulation model based on data must be then carefully implemented. When applied to complex standing structures such as bridges, discrepancies between the computational model and the real system appear as model bias, which hinders the trustworthiness of the digital twin and increases its uncertainty. Classical Bayesian updating approaches aiming to infer the model parameters often fail at compensating for such model bias, leading to overconfident and unreliable predictions. In this paper, two alternative model bias identification approaches are evaluated in the context of their applicability to digital twins of bridges. A modularized version of Kennedy and O'Hagan's approach and another one based on Orthogonal Gaussian Processes are compared with the classical Bayesian inference framework in a set of representative benchmarks. Additionally, two novel extensions are proposed for such models: the inclusion of noise-aware kernels and the introduction of additional variables not present in the computational model through the bias term. The integration of such approaches in the digital twin corrects the predictions, quantifies their uncertainty, estimates noise from unknown physical sources of error and provides further insight into the system by including additional pre-existing information without modifying the computational model.}, language = {en} } @article{BartelsFisikopoulosWeiser, author = {Bartels, Tinko and Fisikopoulos, Vissarion and Weiser, Martin}, title = {Fast Floating-Point Filters for Robust Predicates}, series = {BIT Numerical Mathematics}, volume = {63}, journal = {BIT Numerical Mathematics}, doi = {10.1007/s10543-023-00975-x}, abstract = {Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information systems and computer-aided design. With floating-point arithmetic, these geometric predicates can incur round-off errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetic for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We combine and extend different approaches to filtering, branch reduction, and overflow avoidance that have previously been proposed. We show examples of how this approach produces correct results for data sets that could lead to incorrect predicate results with naive implementations. Our benchmark results demonstrate that our implementation surpasses state-of-the-art implementations.}, language = {en} } @inproceedings{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization}, series = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, volume = {106}, booktitle = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, doi = {10.4230/OASIcs.ATMOS.2022.2}, pages = {1 -- 13}, abstract = {We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen's algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage.}, language = {en} } @article{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Newton's Method for Global Free Flight Trajectory Optimization}, series = {Operations Research Forum}, volume = {4}, journal = {Operations Research Forum}, doi = {10.1007/s43069-023-00238-z}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91846}, abstract = {Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.}, language = {en} } @article{BorndoerferDaneckerWeiser2020, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Free Flight Planning}, series = {Algorithms}, volume = {14}, journal = {Algorithms}, number = {1}, publisher = {MDPI}, issn = {1438-0064}, doi = {10.3390/a14010004}, pages = {4}, year = {2020}, abstract = {We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.}, language = {en} } @inproceedings{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization}, series = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, doi = {10.4230/OASIcs.ATMOS.2023.3}, pages = {3:1 -- 3:6}, abstract = {The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.}, language = {en} } @article{CardereraPokuttaSchuetteetal., author = {Carderera, Alejandro and Pokutta, Sebastian and Sch{\"u}tte, Christof and Weiser, Martin}, title = {CINDy: Conditional gradient-based Identification of Non-linear Dynamics - Noise-robust recovery}, series = {Journal of Computational and Applied Mathematics}, journal = {Journal of Computational and Applied Mathematics}, abstract = {Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative algorithms, the new algorithm shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry.}, language = {en} } @inproceedings{CheginiFroehlyHuynhetal., author = {Chegini, Fatemeh and Froehly, Algiane and Huynh, Ngoc Mai Monica and Pavarino, Luca and Potse, Mark and Scacchi, Simone and Weiser, Martin}, title = {Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution}, series = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, booktitle = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, doi = {10.23967/c.coupled.2023.004}, abstract = {The cardiac extracellular-membrane-intracellular (EMI) model enables the precise geometrical representation and resolution of aggregates of individual myocytes. As a result, it not only yields more accurate simulations of cardiac excitation compared to homogenized models but also presents the challenge of solving much larger problems. In this paper, we introduce recent advancements in three key areas: (i) the creation of artificial, yet realistic grids, (ii) efficient higher-order time stepping achieved by combining low-overhead spatial adaptivity on the algebraic level with progressive spectral deferred correction methods, and (iii) substructuring domain decomposition preconditioners tailored to address the complexities of heterogeneous problem structures. The efficiency gains of these proposed methods are demonstrated through numerical results on cardiac meshes of different sizes.}, language = {en} } @article{CheginiKopanicakovaKrauseetal., author = {Chegini, Fatemeh and Kopanicakova, Alena and Krause, Rolf and Weiser, Martin}, title = {Efficient Identification of Scars using Heterogeneous Model Hierarchies}, series = {EP Europace}, volume = {23}, journal = {EP Europace}, doi = {10.1093/europace/euaa402}, pages = {i113 -- i122}, abstract = {Aims. Detection and quantification of myocardial scars are helpful both for diagnosis of heart diseases and for building personalized simulation models. Scar tissue is generally charac­terized by a different conduction of electrical excitation. We aim at estimating conductivity-related parameters from endocardial mapping data, in particular the conductivity tensor. Solving this inverse problem requires computationally expensive monodomain simulations on fine discretizations. Therefore, we aim at accelerating the estimation using a multilevel method combining electrophysiology models of different complexity, namely the mono­domain and the eikonal model. Methods. Distributed parameter estimation is performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface, subject to the mono­domain model and regularization, leading to a constrained optimization problem. We formulate this optimization problem, including the modeling of scar tissue and different regularizations, and design an efficient iterative solver. We consider monodomain grid hierarchies and monodomain-eikonal model hierarchies in a recursive multilevel trust-region method. Results. From several numerical examples, both the efficiency of the method and the estimation quality, depending on the data, are investigated. The multilevel solver is significantly faster than a comparable single level solver. Endocardial mapping data of realistic density appears to be just sufficient to provide quantitatively reasonable estimates of location, size, and shape of scars close to the endocardial surface. Conclusion. In several situations, scar reconstruction based on eikonal and monodomain models differ significantly, suggesting the use of the more accurate but more expensive monodomain model for this purpose. Still, eikonal models can be utilized to accelerate the computations considerably, enabling the use of complex electrophysiology models for estimating myocardial scars from endocardial mapping data.}, language = {en} } @inproceedings{CheginiKopanicakovaWeiseretal., author = {Chegini, Fatemeh and Kopanicakova, Alena and Weiser, Martin and Krause, Rolf}, title = {Quantitative Analysis of Nonlinear MultifidelityOptimization for Inverse Electrophysiology}, series = {Domain Decomposition Methods in Science and Engineering XXVI}, booktitle = {Domain Decomposition Methods in Science and Engineering XXVI}, publisher = {Springer}, pages = {65 -- 76}, abstract = {The electric conductivity of cardiac tissue determines excitation propagation and is important for quantifying ischemia and scar tissue and for building personalized models. Estimating conductivity distributions from endocardial mapping data is a challenging inverse problem due to the computational complexity of the monodomain equation, which describes the cardiac excitation. For computing a maximum posterior estimate, we investigate different optimization approaches based on adjoint gradient computation: steepest descent, limited memory BFGS, and recursive multilevel trust region methods, which are using mesh hierarchies or heterogeneous model hierarchies. We compare overall performance, asymptotic convergence rate, and pre-asymptotic progress on selected examples in order to assess the benefit of our multifidelity acceleration.}, language = {en} } @inproceedings{CheginiSteinkeWeiser, author = {Chegini, Fatemeh and Steinke, Thomas and Weiser, Martin}, title = {Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods}, abstract = {The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the computations. Here we investigate a different route to spatial adaptivity that is based on nested subset selection for algebraic degrees of freedom in spectral deferred correction methods. This combination of algebraic adaptivity and iterative solvers for higher order collocation time stepping realizes a multirate integration with minimal overhead. This leads to moderate but significant speedups in both monodomain and cell-by-cell models of cardiac excitation, as demonstrated at four numerical examples.}, language = {en} } @misc{DeuflhardKornhuberSanderetal., author = {Deuflhard, Peter and Kornhuber, Ralf and Sander, Oliver and Schiela, Anton and Weiser, Martin}, title = {Mathematics cures virtual patients}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {7 -- 25}, language = {en} } @article{DeuflhardSchielaWeiser, author = {Deuflhard, Peter and Schiela, Anton and Weiser, Martin}, title = {Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia}, series = {Acta Numerica}, volume = {21}, journal = {Acta Numerica}, pages = {307 -- 378}, abstract = {This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator.}, language = {en} } @inproceedings{DeuflhardWeiser1998, author = {Deuflhard, Peter and Weiser, Martin}, title = {Global inexact Newton multilevel FEM for nonlinear elliptic problems}, series = {Multigrid methods V. proceedings of the 5th European multigrid conference, held in Stuttgart, Germany, October 1-4, 1996.}, volume = {3}, booktitle = {Multigrid methods V. proceedings of the 5th European multigrid conference, held in Stuttgart, Germany, October 1-4, 1996.}, editor = {et al. Hackbusch, Wolfgang}, publisher = {Berlin: Springer}, pages = {71 -- 89}, year = {1998}, language = {en} } @book{DeuflhardWeiser2011, author = {Deuflhard, Peter and Weiser, Martin}, title = {Numerische Mathematik 3}, publisher = {de Gruyter, Berlin}, year = {2011}, language = {de} } @book{DeuflhardWeiser2012, author = {Deuflhard, Peter and Weiser, Martin}, title = {Adaptive numerical solution of PDEs}, publisher = {de Gruyter}, address = {Berlin}, year = {2012}, language = {en} } @book{DeuflhardWeiser, author = {Deuflhard, Peter and Weiser, Martin}, title = {Numerische Mathematik 3. Adaptive L{\"o}sung partieller Differentialgleichungen}, edition = {2}, publisher = {de Gruyter}, isbn = {978-3-11-069168-9}, doi = {10.1515/9783110689655}, pages = {456}, language = {de} } @incollection{DeuflhardWeiser1997, author = {Deuflhard, Peter and Weiser, Martin}, title = {Local inexact Newton multilevel FEM for nonlinear elliptic problems}, series = {Computational science for the 21st century}, booktitle = {Computational science for the 21st century}, editor = {et al. Bristeau, M.-O.}, publisher = {Chichester: John Wiley \& Sons.}, pages = {129 -- 138}, year = {1997}, language = {en} } @article{DeuflhardWeiserSeebass2000, author = {Deuflhard, Peter and Weiser, Martin and Seebass, Martin}, title = {A new nonlinear elliptic multilevel FEM in clinical cancer therapy planning}, series = {Comput. Vis. Sci.}, volume = {3}, journal = {Comput. Vis. Sci.}, pages = {115 -- 120}, year = {2000}, language = {en} } @article{DeuflhardWeiserSeebass2000, author = {Deuflhard, Peter and Weiser, Martin and Seebaß, Martin}, title = {A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia}, series = {Comput. Visual. Sci.}, volume = {3}, journal = {Comput. Visual. Sci.}, doi = {10.1007/PL00013546}, pages = {1 -- 6}, year = {2000}, language = {en} } @article{DeuflhardWeiserZachow2006, author = {Deuflhard, Peter and Weiser, Martin and Zachow, Stefan}, title = {Mathematics in Facial Surgery}, series = {AMS Notices}, volume = {53}, journal = {AMS Notices}, number = {9}, pages = {1012 -- 1016}, year = {2006}, language = {en} } @inproceedings{DhanakotiMaddocksWeiser, author = {Dhanakoti, Siva Prasad Chakri and Maddocks, John and Weiser, Martin}, title = {Navigation of Concentric Tube Continuum Robots using Optimal Control}, series = {Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics}, booktitle = {Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics}, doi = {10.5220/0011271000003271}, pages = {146 -- 154}, abstract = {Recently developed Concentric Tube Continuum Robots (CTCRs) are widely exploited in, for example in minimally invasive surgeries which involve navigating inside narrow body cavities close to sensitive regions. These CTCRs can be controlled by extending and rotating the tubes in order to reach a target point or perform some task. The robot must deviate as little as possible from this narrow space and avoid damaging neighbouring tissue. We consider \emph{open-loop} optimal control of CTCRs parameterized over pseudo-time, primarily aiming at minimizing the robot's working volume during its motion. External loads acting on the system like tip loads or contact with tissues are not considered here. We also discussed the inclusion of tip's orientation in the optimal framework to perform some tasks. We recall a quaternion-based formulation of the robot configuration, discuss discretization, develop optimization objectives addressing different criteria, and investigate their impact on robot path planning for several numerical examples. This optimal framework can be applied to any backbone based continuum robots.}, language = {en} } @article{FischerGoetschelWeiser, author = {Fischer, Lisa and G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy data compression reduces communication time in hybrid time-parallel integrators}, series = {Comput. Vis. Sci.}, volume = {19}, journal = {Comput. Vis. Sci.}, number = {1}, doi = {10.1007/s00791-018-0293-2}, pages = {19 -- 30}, abstract = {Parallel in time methods for solving initial value problems are a means to increase the parallelism of numerical simulations. Hybrid parareal schemes interleaving the parallel in time iteration with an iterative solution of the individual time steps are among the most efficient methods for general nonlinear problems. Despite the hiding of communication time behind computation, communication has in certain situations a significant impact on the total runtime. Here we present strict, yet no sharp, error bounds for hybrid parareal methods with inexact communication due to lossy data compression, and derive theoretical estimates of the impact of compression on parallel efficiency of the algorithms. These and some computational experiments suggest that compression is a viable method to make hybrid parareal schemes robust with respect to low bandwidth setups.}, language = {en} } @inproceedings{GanderKrauseWeiseretal., author = {Gander, Lia and Krause, Rolf and Weiser, Martin and Costabal, Francisco and Pezzuto, Simone}, title = {On the Accuracy of Eikonal Approximations in Cardiac Electrophysiology in the Presence of Fibrosis}, series = {Functional Imaging and Modeling of the Heart. FIMH 2023.}, volume = {13958}, booktitle = {Functional Imaging and Modeling of the Heart. FIMH 2023.}, publisher = {Springer, Cham}, doi = {10.1007/978-3-031-35302-4_14}, abstract = {Fibrotic tissue is one of the main risk factors for cardiac arrhythmias. It is therefore a key component in computational studies. In this work, we compare the monodomain equation to two eikonal models for cardiac electrophysiology in the presence of fibrosis. We show that discontinuities in the conductivity field, due to the presence of fibrosis, introduce a delay in the activation times. The monodomain equation and eikonal-diffusion model correctly capture these delays, contrarily to the classical eikonal equation. Importantly, a coarse space discretization of the monodomain equation amplifies these delays, even after accounting for numerical error in conduction velocity. The numerical discretization may also introduce artificial conduction blocks and hence increase propagation complexity. Therefore, some care is required when comparing eikonal models to the discretized monodomain equation.}, language = {en} } @article{GellermannWeihrauchChoetal.2006, author = {Gellermann, Johanna and Weihrauch, Mirko and Cho, C. and Wlodarczyk, Waldemar and F{\"a}hling, Horst and Felix, Roland and Budach, Volker and Weiser, Martin and Nadobny, Johanna and Wust, Peter}, title = {Comparison of MR-thermography and planning calculations in phantoms}, series = {Medical Physics}, volume = {33}, journal = {Medical Physics}, pages = {3912 -- 3920}, year = {2006}, language = {en} } @article{GriesseWeiser2008, author = {Griesse, Roland and Weiser, Martin}, title = {On the Interplay Between Interior Point Approximation and Parametric Sensitivities in Optimal Control}, series = {Journal of Mathematical Analysis and Applications}, journal = {Journal of Mathematical Analysis and Applications}, pages = {771 -- 793}, year = {2008}, language = {en} } @article{GaenzlerVolkweinWeiser2006, author = {G{\"a}nzler, Tobias and Volkwein, S. and Weiser, Martin}, title = {SQP methods for parameter identification problems arising in hyperthermia}, series = {Optim. Methods Softw.}, volume = {21}, journal = {Optim. Methods Softw.}, number = {6}, pages = {869 -- 887}, year = {2006}, language = {en} } @inproceedings{GoetschelHoehneKolkoorietal., author = {G{\"o}tschel, Sebastian and H{\"o}hne, Christian and Kolkoori, Sanjeevareddy and Mitzscherling, Steffen and Prager, Jens and Weiser, Martin}, title = {Ray Tracing Boundary Value Problems: Simulation and SAFT Reconstruction for Ultrasonic Testing}, series = {Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)}, booktitle = {Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)}, language = {en} } @inproceedings{GoetschelMaierhoferMuelleretal., author = {G{\"o}tschel, Sebastian and Maierhofer, Christiane and M{\"u}ller, Jan and Rothbart, Nick and Weiser, Martin}, title = {Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites}, series = {Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)}, booktitle = {Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)}, language = {en} } @article{GoetschelNagaiahKunischetal., author = {G{\"o}tschel, Sebastian and Nagaiah, Chamakuri and Kunisch, Karl and Weiser, Martin}, title = {Lossy Compression in Optimal Control of Cardiac Defibrillation}, series = {J. Sci. Comput.}, volume = {60}, journal = {J. Sci. Comput.}, number = {1}, doi = {10.1007/s10915-013-9785-x}, pages = {35 -- 59}, abstract = {This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.}, language = {en} } @article{GoetschelSchielaWeiser, author = {G{\"o}tschel, Sebastian and Schiela, Anton and Weiser, Martin}, title = {Kaskade 7 - a Flexible Finite Element Toolbox}, series = {Computers and Mathematics with Applications}, volume = {81}, journal = {Computers and Mathematics with Applications}, doi = {10.1016/j.camwa.2020.02.011}, pages = {444 -- 458}, abstract = {Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the \textsc{Dune} interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.}, language = {en} } @inproceedings{GoetschelTycowiczPolthieretal., author = {G{\"o}tschel, Sebastian and Tycowicz, Christoph von and Polthier, Konrad and Weiser, Martin}, title = {Reducing Memory Requirements in Scientific Computing and Optimal Control}, series = {Multiple Shooting and Time Domain Decomposition Methods}, booktitle = {Multiple Shooting and Time Domain Decomposition Methods}, editor = {Carraro, T. and Geiger, M. and Koerkel, S. and Rannacher, R.}, publisher = {Springer}, pages = {263 -- 287}, language = {en} } @article{GoetschelWeiser, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {State Trajectory Compression in Optimal Control}, series = {PAMM}, volume = {10}, journal = {PAMM}, number = {1}, doi = {10.1002/pamm.201010282}, pages = {579 -- 580}, abstract = {In optimal control problems with nonlinear time-dependent 3D PDEs, the computation of the reduced gradient by adjoint methods requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. Since the state enters into the adjoint equation, the storage of a 4D discretization is necessary. We propose a lossy compression algorithm using a cheap predictor for the state data, with additional entropy coding of prediction errors. Analytical and numerical results indicate that compression factors around 30 can be obtained without exceeding the FE discretization error.}, language = {en} } @article{GoetschelWeiser, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy Compression for PDE-constrained Optimization: Adaptive Error Control}, series = {Comput. Optim. Appl.}, volume = {62}, journal = {Comput. Optim. Appl.}, number = {1}, publisher = {Springer}, pages = {131 -- 155}, abstract = {For the solution of optimal control problems governed by nonlinear parabolic PDEs, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the ad-joint equation. The state enters into the adjoint equation, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results which are accurate enough, in many case very fine discretizations in time and space are necessary, which leads to a significant amount of data to be stored and transmitted to mass storage. Lossy compression methods were developed to overcome the storage problem by reducing the accuracy of the stored trajectories. The inexact data induces errors in the reduced gradient and reduced Hessian. In this paper, we analyze the influence of such a lossy trajectory compression method on Newton-CG methods for optimal control of parabolic PDEs and design an adaptive strategy for choosing appropriate quantization tolerances.}, language = {en} } @article{GoetschelWeiser, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Compression Challenges in Large Scale Partial Differential Equation Solvers}, series = {Algorithms}, volume = {12}, journal = {Algorithms}, number = {9}, doi = {10.3390/a12090197}, pages = {197}, abstract = {Solvers for partial differential equations (PDEs) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that need to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to the relatively small arithmetic intensity, and increasingly due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers over the recent decades. This paper surveys data compression challenges and discusses examples of corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to the main memory. We illustrate concepts for particular methods, with examples, and give references to alternatives.}, language = {en} } @misc{GoetschelWeiserMaierhoferetal., author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina}, title = {Data Enhancement for Active Thermography}, series = {E-book Proceedings, 11th International Conference on Quantitative Infrared Thermography, Naples}, journal = {E-book Proceedings, 11th International Conference on Quantitative Infrared Thermography, Naples}, editor = {Cardone, Gennaro}, abstract = {Pulse thermography is a non-destructive testing method based on infrared imaging of transient thermal patterns. Heating the surface of the structure under test for a short period of time generates a non-stationary temperature distribution and thus a thermal contrast between the defect and the sound material. Due to measurement noise, preprocessing of the experimental data is necessary, before reconstruction algorithms can be applied. We propose a decomposition of the measured temperature into Green's function solutions to eliminate noise.}, language = {en} } @article{GoetschelWeiserMaierhoferetal., author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina and R{\"o}llig, Mathias}, title = {Fast Defect Shape Reconstruction Based on the Travel Time in Pulse Thermography}, series = {Nondestructive Testing of Materials and Structures}, volume = {6}, journal = {Nondestructive Testing of Materials and Structures}, pages = {83 -- 89}, language = {en} } @misc{GoetschelWeiserSchiela, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Schiela, Anton}, title = {Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox}, series = {Advances in DUNE}, journal = {Advances in DUNE}, editor = {Dedner, A. and Flemisch, B. and Kl{\"o}fkorn, R.}, publisher = {Springer}, pages = {101 -- 112}, abstract = {This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.}, language = {en} } @misc{GuentherLameckerWeiser, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Direct LDDMM of Discrete Currents with Adaptive Finite Elements}, series = {Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability}, journal = {Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability}, editor = {Pennec, X. and Joshi, S. and Nielsen, M.}, pages = {1 -- 14}, abstract = {We consider Large Deformation Diffeomorphic Metric Mapping of general \$m\$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete \$m\$-current attributes.}, language = {en} } @article{GuentherLameckerWeiser, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Flexible Shape Matching with Finite Element Based LDDMM}, series = {International Journal of Computer Vision}, volume = {105}, journal = {International Journal of Computer Vision}, number = {2}, doi = {10.1007/s11263-012-0599-3}, pages = {128 -- 143}, abstract = {We consider Large Deformation Diffeomorphic Metric Mapping of general \$m\$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete \$m\$-current attributes.}, language = {en} } @article{HammerschmidtSchneiderSantiagoetal., author = {Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Santiago, Xavier Garcia and Zschiedrich, Lin and Weiser, Martin and Burger, Sven}, title = {Solving inverse problems appearing in design and metrology of diffractive optical elements by using Bayesian optimization}, series = {Proc. SPIE}, volume = {10694}, journal = {Proc. SPIE}, doi = {10.1117/12.2315468}, pages = {1069407}, language = {en} } @article{HammerschmidtWeiserSantiagoetal., author = {Hammerschmidt, Martin and Weiser, Martin and Santiago, Xavier Garcia and Zschiedrich, Lin and Bodermann, Bernd and Burger, Sven}, title = {Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion}, series = {Proc. SPIE}, volume = {10330}, journal = {Proc. SPIE}, doi = {10.1117/12.2270596}, pages = {1033004}, language = {en} } @article{HorenkoWeiserSchmidtetal.2004, author = {Horenko, Illia and Weiser, Martin and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Fully Adaptive Propagation of the Quantum-Classical Liouville Equation}, series = {J. Chem. Phys.}, volume = {120}, journal = {J. Chem. Phys.}, number = {19}, doi = {10.1063/1.1691015}, pages = {8913 -- 8923}, year = {2004}, language = {en} } @article{HuynhCheginiPavarinoetal., author = {Huynh, Ngoc and Chegini, Fatemeh and Pavarino, Luca and Weiser, Martin and Scacchi, Simone}, title = {Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model}, series = {SIAM Journal on Scientific Computing}, volume = {45}, journal = {SIAM Journal on Scientific Computing}, number = {6}, pages = {A2836 -- A2857}, abstract = {A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of hybrid Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. The latter are different from the classical Bidomain and Monodomain cardiac models based on homogenized descriptions of the cardiac tissue at the macroscopic level, and therefore they allow the representation of individual cardiac cells, cell aggregates, damaged tissues and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models have discontinuous global solutions across the cell boundaries, hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells (subdomains) without influencing the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters.}, language = {en} } @inproceedings{KrauseWeiser, author = {Krause, Rolf and Weiser, Martin}, title = {Multilevel augmented Lagrangian solvers for overconstrained contact formulations}, series = {ESAIM: ProcS}, volume = {71}, booktitle = {ESAIM: ProcS}, doi = {10.1051/proc/202171175}, pages = {175 -- 184}, abstract = {Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems.}, language = {en} } @article{LubkollSchielaWeiser, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An optimal control problem in polyconvex hyperelasticity}, series = {SIAM J. Control Opt.}, volume = {52}, journal = {SIAM J. Control Opt.}, number = {3}, doi = {10.1137/120876629}, pages = {1403 -- 1422}, abstract = {We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented.}, language = {en} }