Efficient Assembly of Sparse Matrices Using Hashing

Abstract

In certain applications the non-zero elements of large sparse matrices are formed by adding several smaller contributions in random order before the final values of the elements are known. For some sparse matrix representations this procedure is laborious. We present an efficient method for assembling large irregular sparse matrices where the non-zero elements have to be assembled by adding together contributions and updating the individual elements in random order. A sparse matrix is stored in a hash table, which allows an efficient method to search for an element. Measurements show that for a sparse matrix with random elements the hash-based representation performs almost 7 times faster than the compressed row format (CRS) used in the PETSc library. Once the sparse matrix has been assembled we transfer the matrix to e.g. CRS for matrix manipulations.