Abstract
The finite element code Kaskade has been developed for the solution of partial differential equations in one, two, and 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.
One major concept of the implementation is the separation of ‘geometric’ and ‘algebraic’ entities. The former ones mainly comprise typical problem-dependent classes like the mesh, the finite element, and the materials. The mesh structure and node distribution may be rather complex due to the nested refinement levels created in the adaptive solution process. By using a global node-numbering strategy we transfer the geometry-based features into algebraic structures; the latter include special sparse matrix classes and vector templates.
Beyond the formal description of the code we present an application arising in a current research project. Here a real-life problem has to be solved, involving the calculation of electromagnetic fields and temperature distributions in human bodies in order to support hyperthermia treatment planning in a clinical environment.
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Beck, R., Erdmann, B., Roitzsch, R. (1997). An Object-Oriented Adaptive Finite Element Code: Design Issues and Applications in Hyperthermia Treatment Planning. In: Arge, E., Bruaset, A.M., Langtangen, H.P. (eds) Modern Software Tools for Scientific Computing. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1986-6_5
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DOI: https://doi.org/10.1007/978-1-4612-1986-6_5
Publisher Name: Birkhäuser, Boston, MA
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