For smooth problems spectral element methods (SEM) exhibit exponential convergence and have been very successfully used in practical problems. However, in many engineering and scientific applications we frequently encounter the numerical solutions of elliptic boundary value problems in non-smooth domains which give rise to singularities in the solution. In such cases the accuracy of the solution obtained by SEM deteriorates and they offer no advantages over low order methods. A new Parallel h-p Spectral Element Method is presented which resolves this form of singularity by employing a geometric mesh in the neighborhood of the corners and gives exponential convergence with asymptotically faster results than conventional methods. The normal equations are solved by the Preconditioned Conjugate Gradient (PCG) method. Except for the assemblage of the resulting solution vector, all computations are done on the element level and we don't need to compute and store mass and stiffness like matrices. The technique to compute the preconditioner is quite simple and very easy to implement. The method is based on a parallel computer with distributed memory and the library used for message passing is MPI. Load balancing issues are discussed and the communication involved among the processors is shown to be quite small.
|Title of host publication||High Performance Computing — HiPC 2002|
|Subtitle of host publication||9th International Conference Bangalore, India, December 18–21, 2002 Proceedings|
|Editors||Sartaj Sahni, Viktor K. Prasanna, Uday Shukla|
|Place of Publication||Berlin, Germany|
|Number of pages||11|
|Publication status||Published - 2002|
|Name||Lecture Notes In Computer Science|