×

Numerical engineering: Design of PDE black-box solvers. (English) Zbl 0978.65082

The author designs a partial differential equation (PDE) black-box solver for systems of nonlinear elliptic and parabolic PDEs that is at the same time robust and efficient using a finite difference method on an unstructured finite-element-method grid.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
35K55 Nonlinear parabolic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs

Software:

VECFEM; PELLPACK; LINSOL
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] L. Grosz, C. Roll, W. Schönauer, Black-box solver for the solution of general nonlinear functional equations by mixed FEM, in: M. Krizek, P. Neittaanmäki, R. Stenberg (Eds.), Finite Element Methods \(,\); L. Grosz, C. Roll, W. Schönauer, Black-box solver for the solution of general nonlinear functional equations by mixed FEM, in: M. Krizek, P. Neittaanmäki, R. Stenberg (Eds.), Finite Element Methods \(,\) · Zbl 0812.65097
[2] H. Häfner, W. Schönauer, R. Weiss, The parallel and portable linear solver package linsol,; H. Häfner, W. Schönauer, R. Weiss, The parallel and portable linear solver package linsol,
[3] Häfner, H.; Schönauer, W.; Weiss, R., The program package linsol — basic concepts and realization, Appl. Numer. Math., 30, 2-3, 213-224 (1999)
[4] Houstis, E. N.; Rice, J. R.; Weerawarana, S.; Catlin, A. C.; Papachiou, P.; Gaitatzes, M., pellpack: a problem solving environment for PDE based applications on multicomputer platforms, ACM Trans. Math. Soft., 24, 1, 30-73 (1998) · Zbl 0917.65097
[5] pellpackhttp://www.cs.purdue,edu/research/cse/gifs/pellpack/foreign.gif; pellpackhttp://www.cs.purdue,edu/research/cse/gifs/pellpack/foreign.gif
[6] J.R. Rice, An agent-based architecture for solving partial differential equations, SIAM News 31 6 (1998) 1 and 6-7.; J.R. Rice, An agent-based architecture for solving partial differential equations, SIAM News 31 6 (1998) 1 and 6-7.
[7] M. Scbmauder, W. Schönauer, A fully vectorized black-box solver for 2-D and 3-D partial differential equations, in: R. Vichnevetski, D. Knight, G. Richter (Eds.), Advances in Computer Methods for Partial Differential Equations \(—\); M. Scbmauder, W. Schönauer, A fully vectorized black-box solver for 2-D and 3-D partial differential equations, in: R. Vichnevetski, D. Knight, G. Richter (Eds.), Advances in Computer Methods for Partial Differential Equations \(—\)
[8] W. Schönauer, Scientific Computing on Vector Computers, North-Holland, Amsterdam, 1987.; W. Schönauer, Scientific Computing on Vector Computers, North-Holland, Amsterdam, 1987.
[9] W. Schönauer, H. Weiss, R. Linsol, a parallel iterative linear solver package of generalized CG-type for sparse matrices, in: M. Heath et al. (Eds.), Proceedings of the Eighth SIAM Conference on Parallel Processing for Scientific Computing, SIAM, Philadelphia, PA, CD-ROM, 1997, 8 pp, ISBN 0-89871-395-1.; W. Schönauer, H. Weiss, R. Linsol, a parallel iterative linear solver package of generalized CG-type for sparse matrices, in: M. Heath et al. (Eds.), Proceedings of the Eighth SIAM Conference on Parallel Processing for Scientific Computing, SIAM, Philadelphia, PA, CD-ROM, 1997, 8 pp, ISBN 0-89871-395-1.
[10] W. Schönauer, Generation of difference and error formulae of arbitrary consistency order on an unstructured grid, ZAMM’78, Supplement 3, 1998, pp. 1061-1062.; W. Schönauer, Generation of difference and error formulae of arbitrary consistency order on an unstructured grid, ZAMM’78, Supplement 3, 1998, pp. 1061-1062.
[11] W. Schönauer, Scientific Supercomputing: Architecture and Use of Shared and Distributed Memory Parallel Computers. Internet book. URL: http://www.uni-karlsruhe.de/Uni/RZ/Personen/rz03/book/; W. Schönauer, Scientific Supercomputing: Architecture and Use of Shared and Distributed Memory Parallel Computers. Internet book. URL: http://www.uni-karlsruhe.de/Uni/RZ/Personen/rz03/book/
[12] W. Schönauer, T. Adolph, How we solve PDEs? submitted for publication.; W. Schönauer, T. Adolph, How we solve PDEs? submitted for publication.
[13] H. Stetter, Vienna, private communication in many fruitful personal discussions.; H. Stetter, Vienna, private communication in many fruitful personal discussions.
[14] R. Weiss, Parameter-free iterative linear solvers, Mathematical Research, Vol. 97, Akademie-Verlag, Berlin, Germany.; R. Weiss, Parameter-free iterative linear solvers, Mathematical Research, Vol. 97, Akademie-Verlag, Berlin, Germany. · Zbl 0858.65031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.