Roman Geus

Towards a fast parallel sparse symmetric matrix-vector multiplication

Abstract The sparse matrix–vector product is an important computational kernel that runs ineffectively on many computers with super-scalar RISC processors. In this paper we analyse the performance of the sparse matrix–vector product with symmetric matrices originating from the FEM and describe techniques that lead to a fast implementation. It is shown how these optimisations can be incorporated into an efficient parallel implementation using message-passing. We conduct numerical experiments on many different machines and show that our optimisations speed up the sparse matrix–vector multiplication substantially.

Towards a fast parallel sparse matrix-vector multiplication.

The sparse matrix-vector product is an important computational kernel that runs ineffectively on many computers with super-scalar RISC processors. In this paper we analyse the performance of the sparse matrix-vector product with symmetric matrices originating from the FEM and describe techniques that lead to a fast implementation. It is shown how these optimisations can be incorporated into an efficient parallel implementation using messagepassing. We conduct numerical experiments on many different machines and show that our optimisations speed up the sparse matrix-vector multiplication substantially.

A comparison of solvers for large eigenvalue problems occuring in the design of resonant cavities

We present experiments with various solvers for large sparse generalized symmetric matrix eigenvalue problems. These problems occur in the computation of a few of the lowest frequencies of standing electromagnetic waves in resonant cavities with the finite element method. The solvers investigated are (1) subspace iteration, (2) block Lanczos algorithm, (3) implicitly restarted Lanczos algorithm and (4) Jacobi–Davidson algorithm. The experiments have been conducted on a Hewlett-Packard Exemplar S-Class system. Copyright

On a parallel multilevel preconditioned Maxwell eigensolver

We report on a parallel implementation of the Jacobi–Davidson (JD) to compute a few eigenpairs of a large real symmetric generalized matrix eigenvalue problem

TWO-LEVEL HIERARCHICAL BASIS PRECONDITIONERS FOR COMPUTING EIGENFREQUENCIES OF CAVITY RESONATORS WITH THE FINITE ELEMENT METHOD

A \mathbf{x} = \lambda M \mathbf{x}, \qquad C^T \mathbf{x} = \mathbf{0}.

Solving Maxwell eigenvalue problems for accelerating cavities

The eigenvalue problem stems from the design of cavities of particle accelerators. It is obtained by the finite element discretization of the time-harmonic Maxwell equation in weak form by a combination of Nedelec (edge) and Lagrange (node) elements. We found the Jacobi–Davidson (JD) method to be a very effective solver provided that a good preconditioner is available for the correction equations that have to be solved in each step of the JD iteration. The preconditioner of our choice is a combination of a hierarchical basis preconditioner and a smoothed aggregation AMG preconditioner. It is close to optimal regarding iteration count and scales with regard to memory consumption. The parallel code makes extensive use of the Trilinos software framework.

Eigenvalue solvers for electromagnetic fields in cavities

We present experiments with two new solvers for large sparse symmetric matrix eigenvalue problems: (1) the implicitly restarted Lanczos algorithm and (2) the Jacobi-Davidson algorithm. The eigenvalue problems originate from in the computation of a few of the lowest frequencies of standing electromagnetic waves in cavities that have been discretized by the finite element method. The experiments have been conducted on up to 12 processors of an HP Exemplar X-Class multiprocessor computer.

A Comparison of Solvers for Large Eigenvalue Problems Originating from Maxwell's Equations

We report on experiments conducted with the implicitly restarted Lanczos algorithm for computing a few of the lowest frequencies of standing electromagnetic waves in resonant cavities with the nite element method. The linear systems that are caused by the shift and invert spectral transformation are solved by means of two-level hierarchical basis preconditioners.