Parallel Numerical Algorithms for 3D Parabolic Problem with Nonlocal Boundary Condition

Authors:
Raimondas Čiegis
Affiliations:
Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania, e-mail: rc@fm.vtu.lt
Venue:
Informatica
Year:
2006

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Abstract

Three parallel algorithms for solving the 3D problem with nonlocal boundary condition are considered. The forward and backward Euler finite-difference schemes, and LOD scheme are typical representatives of three general classes of parallel algorithms used to solve multidimensional parabolic initial-boundary value problems. All algorithms are modified to take into account additional nonlocal boundary condition. The algorithms are implemented using the parallel array object tool ParSol, then a parallel algorithm follows semi-automatically from the serial one. Results of computational experiments are presented and the accuracy and efficiency of the presented parallel algorithms are tested.