Refine
Year of publication
Document Type
- ZIB-Report (18)
Language
- English (18)
Has Fulltext
- yes (18)
Is part of the Bibliography
- no (18)
Keywords
Institute
- ZIB Allgemein (18) (remove)
In this paper we present a self--adaptive finite element method to solve flame propagation problems in 3D. An implicit time integrator of Rosenbrock type is coupled with a multilevel approach in space. The proposed method is applied to an unsteady thermo--diffusive combustion model to demonstrate its potential for the solution of complicated problems.
KARDOS solves nonlinear evolution problems in 1, 2, and 3D. An adaptive multilevel finite element algorithm is used to solve the spatial problems arising from linearly implicit discretization methods in time. Local refinement and derefinement techniques are used to handle the development of the mesh over time. The software engineering techniques used to implement the modules of the KASKADE toolbox are reviewed and their application to the extended problem class is described. A notification system and dynamic construction of records are discussed and their values for the implementation of a mesh transfer operation are shown. The need for low-level and high--level interface elements of a module is discussed for the assembling procedure of KARDOS. At the end we will summarize our experiences.
The transient heating in an unsymmetrical coated hot--strip sensor was simulated with a self--adaptive finite element method. The first tests of this model show that it can determine with a small error the thermal conductivity of liquids, from the transient temperature rise in the hot--strip, deposited in a substrate and coated by an alumina spray.
The correlation of the inner architecture of bone and its functional loading was already stated by Wolff in 1892. Our objective is to demonstrate this interdependence in the case of the human mandible. For this purpose, stress/strain profiles occuring at a human lateral bite were simulated. Additionally, by a combination of computer graphics modules, a three--dimensional volumetric visualization of bone mineral density could be given. Qualitative correspondences between the density profile of the jaw and the simulated stress/strain profiles could be pointed out. In the long run, this might enable the use of the simulation for diagnosis and prognosis. The solution of the underlying partial differential equations describing linear elastic material behaviour was provided by an adaptive finite element method. Estimates of the discretization errors, local grid refinement, and multilevel techniques guaranteed the reliability and efficiency of the method.
The KASKADE toolbox defines an interface to a set of C subroutines which can be used to implement adaptive multilevel Finite Element Methods solving systems of elliptic equations in two and three space dimensions. The manual contains the description of the data structures and subroutines. The main modules of the toolbox are a runtime environment, triangulation and node handling, assembling, direct and iterative solvers for the linear systems, error estimators, refinement strategies, and graphic utilities. Additionally, we included appendices on the basic command language interface, on file formats, and on the definition of the partial differential equations which can be solved. The software is available on the ZIB ftp--server {\tt elib} in the directory {\tt pub/kaskade}. TR 93--5 supersedes TR 89--4 and TR 89--05.
KASKADE 3.0 User's Guide
(1995)
KASKADE 3.x was developed for the solution of partial differential equations in one, two, or three space dimensions. Its object-oriented implementation concept is based on the programming language C++$\,$.~Adaptive finite element techniques are employed to provide solution procedures of optimal computational complexity. This implies a posteriori error estimation, local mesh refinement and multilevel preconditioning. The program was designed both as a platform for further developments of adaptive multilevel codes and as a tool to tackle practical problems. Up to now we have implemented scalar problem types like stationary or transient heat conduction. The latter one is solved with the Rothe method, enabling adaptivity both in space and time. Some nonlinear phenomena like obstacle problems or two-phase Stefan problems are incorporated as well. Extensions to vector-valued functions and complex arithmetic are provided. This report helps to work with KASKADE Especially we \begin{itemize} \setlength{\parskip}{0ex} \item [{\bf --}] study a set of examples, \item [{\bf --}] explain how to define a user's problem and \item [{\bf --}] introduce a graphical user interface. \end{itemize} We are extending this guide continuously. The latest version is available by network.
KASKADE 3.0 was developed for the solution of partial differential equations in one, two, or three space dimensions. Its object-oriented implementation concept is based on the programming language C++$\,$.~Adaptive finite element techniques are employed to provide solution procedures of optimal computational complexity. This implies a posteriori error estimation, local mesh refinement and multilevel preconditioning. The program was designed both as a platform for further developments of adaptive multilevel codes and as a tool to tackle practical problems. Up to now we have implemented scalar problem types like stationary or transient heat conduction. The latter one is solved with the Rothe method, enabling adaptivity both in space and time. Some nonlinear phenomena like obstacle problems or two-phase Stefan problems are incorporated as well. Extensions to vector-valued functions and complex arithmetic are provided. %Such free boundary problems ... We have implemented several iterative solvers for both symmetric and unsymmetric systems together with multiplicative and additive multilevel preconditioners. Systems arising from the nonlinear problems can be solved with lately developed monotone multigrid methods. %An object-oriented concept was chosen for KASKADE~3.0, based on the programming %language C++$\,$. This should provide the desired extensibilty and clearly %reflect the structure of the code. %A direct sparse matrix solver (Harwell MA28) is included.
The C-implementation of KASKADE, an adaptive solver for linear elliptic differential equations in 2D, is object of a set of numerical experiments to analyze the use of resources (time and memory) with respect to numerical accuracy. We study the dependency of the reliability, robustness, and efficiency of the program from the parameters controlling the algorithm.
KARDOS - User"s Guide
(2002)
The adaptive finite element code {\sc Kardos} solves nonlinear parabolic systems of partial differential equations. It is applied to a wide range of problems from physics, chemistry, and engineering in one, two, or three space dimensions. The implementation is based on the programming language C. Adaptive finite element techniques are employed to provide solvers of optimal complexity. This implies a posteriori error estimation, local mesh refinement, and preconditioning of linear systems. Linearely implicit time integrators of {\em Rosenbrock} type allow for controlling the time steps adaptively and for solving nonlinear problems without using {\em Newton's} iterations. The program has proved to be robust and reliable. The user's guide explains all details a user of {\sc Kardos} has to consider: the description of the partial differential equations with their boundary and initial conditions, the triangulation of the domain, and the setting of parameters controlling the numerical algorithm. A couple of examples makes familiar to problems which were treated with {\sc Kardos}. We are extending this guide continuously. The latest version is available by network: {\begin{rawhtml} <A href="http://www.zib.de/Numerik/software/kardos/"> <i> Downloads.</i></a> \end{rawhtml}}
We describe an optimization process specially designed for regional hyperthermia of deep seated tumors in order to achieve desired steady--state temperature distributions. A nonlinear three--dimensional heat transfer model based on temperature--dependent blood perfusion is applied to predict the temperature. Using linearly implicit methods in time and adaptive multilevel finite elements in space, we are able to integrate efficiently the instationary nonlinear heat equation with high accuracy. Optimal heating is obtained by minimizing an integral object function which measures the distance between desired and model predicted temperatures. A sequence of minima is calculated from successively improved constant--rate perfusion models employing a damped Newton method in an inner iteration. We compare temperature distributions for two individual patients calculated on coarse and fine spatial grids and present numerical results of optimizations for a Sigma 60 Applicator of the BSD 2000 Hyperthermia System.