@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} } @article{WeiserGoetschel, author = {Weiser, Martin and G{\"o}tschel, Sebastian}, title = {State Trajectory Compression for Optimal Control with Parabolic PDEs}, series = {SIAM J. Sci. Comput.}, volume = {34}, journal = {SIAM J. Sci. Comput.}, number = {1}, doi = {10.1137/11082172X}, pages = {A161 -- A184}, abstract = {In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient.}, 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{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{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{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} } @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} } @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} }