Abstract
Numerical solutions of a large sparse linear system of equations are often appeared in numerical simulations. In many cases, the computational time to solve it accounts for a large portion of the total simulation time. Thus, reducing its time is very important. We studied a relaxed supernodal multifrontal method for the direct method of symmetric positive definite linear systems, and numerical experiments on test matrices from the University of Florida Sparse Matrix Collection are presented. We implemented two codes. One is naive implementation which is called basic code. The other is enhanced code which is modified from the basic code in terms of reducing the number of data movement of frontal and update matrices. We found two facts. Firstly, enhanced code is better than basic code in terms of memory storage. Secondly, the performance of this method depends on a relaxation parameter which coalesces the supernodes. Furthermore, this optimal parameter depends on matrices, detailed implementation, and machine architecture.
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