Abstract: A parallel-computing strategy was presented to solve the large-scale heat equations. The distributed memory and compressed matrices technology was adopted for both the process of storage and evaluation of largcscale sparse matrices. All kinds of Krylov subspace methods and preconditioners were introduced to assemble and solve the linear systems of ectuations. The code implementation of this strategy was written in high-level abstractions based on object oriented technology which promotes code reuse, flexibility and helps to decouple issues of parallelism from algorithm choices. The experiments carried on Linux clusters demonstrate that this strategy has achieved desirable speedup and efficicncy.

Key words: Heat equations,Partial differential equations,Finite difference methods,Parallel algorithm