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Parallel, fully automatic \(hp\)-adaptive \(2d\) finite element package. (English) Zbl 1093.65113

Summary: This paper presents a description of par2Dhp – a 2D, parallel fully automatic \(hp\)-adaptive finite element code. The parallel implementation is an extension of the sequential code 2Dhp90, which generates fully automatic \(hp\)-approximations for solutions of various boundary value problems. The presented work addresses parallelization of each stage of the automatic \(hp\)-adaptive algorithm, including decomposition of the computational domain, load balancing and data redistribution, a parallel frontal solver, and algorithms for parallel mesh refinement and mesh reconciliation.
The application was written in Fortran 90 and MPI, and the load balancing is done through an interface with the Zoltan library. Numerical results are presented for the model L-shape domain problem, and a highly anisotropic heat conduction (battery) problem from Sandia National Laboratories.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
65Y05 Parallel numerical computation
78A45 Diffraction, scattering
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:

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