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

Article type: Research Article

Authors: Čiegis, Raimondas

Affiliations: Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania, e-mail: rc@fm.vtu.lt

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.

Keywords: parallel algorithms, finite-difference schemes, parabolic problems, nonlocal conditions

Journal: Informatica, vol. 17, no. 3, pp. 309-324, 2006