Hardware-efficient building blocks for sparse linear algebra and stencil solvers

Description / Outline

The solution of large, sparsely populated systems of equations and eigenvalue problems is typically done by iterative methods.  This research area deals with the efficient implementation, optimization and parallelization of the most important basic building blocks of such iterative solvers. The focus is on the multiplication of a large sparse matrix with one or more vector(s) (SpMV). Both matrix-free representations for regular matrices, such as those occurring in the discretization of partial differential equations ("stencils"), and the generic case of a general SpMV with a stored matrix are considered. Our work on the development and implementation of optimized building blocks for SpMV-based solvers includes hardware-efficient algorithms, data access optimizations (spatial and temporal blocking), and efficient and portable data structures. Our structured performance engineering process is employed in this context.