Using a multifrontal sparse solver in a high performance, finite element code

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.

[1]  Robert Schreiber,et al.  A New Implementation of Sparse Gaussian Elimination , 1982, TOMS.

[2]  William G. Poole,et al.  An algorithm for reducing the bandwidth and profile of a sparse matrix , 1976 .

[3]  Roger Grimes,et al.  The influence of relaxed supernode partitions on the multifrontal method , 1989, TOMS.

[4]  Barry W. Peyton,et al.  Progress in Sparse Matrix Methods for Large Linear Systems On Vector Supercomputers , 1987 .

[5]  Alan George,et al.  The Evolution of the Minimum Degree Ordering Algorithm , 1989, SIAM Rev..

[6]  John K. Reid,et al.  The Multifrontal Solution of Indefinite Sparse Symmetric Linear , 1983, TOMS.

[7]  B. Hager,et al.  Coupling of mantle temperature anomalies and the flow pattern in the core: interpretation based on simple convection calculations , 1989 .

[8]  J. A. George.  Computer implementation of the finite element method , 1971 .

[9]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[10]  Iain S. Duff,et al.  Parallel implementation of multifrontal schemes , 1986, Parallel Comput..

[11]  A. George.  Nested Dissection of a Regular Finite Element Mesh , 1973 .

[12]  Bradford H. Hager,et al.  Conman: vectorizing a finite element code for incompressible two-dimensional convection in the Earth's mantle , 1990 .

[13]  Robert F. Lucas,et al.  A Parallel Solution Method for Large Sparse Systems of Equations , 1987, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.