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A parallel adaptive finite-element package based on ALBERTA. (English) Zbl 1154.65091
Summary: ALBERTA, a sequential adaptive finite-element toolbox, is being used widely in the fields of scientific and engineering computation, especially in the numerical simulation of electromagnetics. But the nature of sequentiality has become the bottle-neck while solving large scale problems. So we develop a parallel adaptive finite-element package based on ALBERTA, using ParMETIS and PETSc. The package is able to deal with any problem that ALBERT solved. Furthermore, it is suitable for distributed memory parallel computers including PC clusters.
In this paper, we present the implementation of the package in detail, and address several key algorithms and strategies of parallelization. Finally, some numerical experiments are given to show the performance and scalability of our package.
MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65Y05 Parallel numerical computation
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65Y15 Packaged methods for numerical algorithms
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References:
[1] Aggarwal R., METIS – family of multilevel partioning algorithms (2003)
[2] Balay S., PETSc – portable, extensible toolkit for scientific computation (2003)
[3] DOI: 10.1016/0377-0427(94)90034-5 · Zbl 0823.65119 · doi:10.1016/0377-0427(94)90034-5
[4] Liu Q., Chin. J. Comput. Phys. 5 pp 399– (2005)
[5] DOI: 10.1016/0377-0427(91)90226-A · Zbl 0733.65066 · doi:10.1016/0377-0427(91)90226-A
[6] Mitchell W. F., Unified multilevel adaptive finite element methods for elliptic problems (1988)
[7] Schmidt A., Design Of Adaptive Finite Element Software: The Finite Element Toolbox ALBERTA (2005) · Zbl 1068.65138
[8] Schmidt A., ALBERTA – an adaptive hierarchical finite element toolbox (2004)
[9] Sewell E. G., Automatic generation of triangulation for piecewise polynomial approximation (1972)
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