International Business Machines Corporation
DETERMINATION AND USE OF SPECTRAL EMBEDDINGS OF LARGE-SCALE SYSTEMS BY SUBSTRUCTURING

Abstract:

A device solves for eigenvalues of a matrix system. The device performs a domain decomposition of a matrix system into non-overlapping subdomains and a reordering of matrices of the matrix system. An interface variable projection subspace associated with interface variables of an adjacency graph of the matrix system is created. The interface variables are related to nodes of the adjacency graph which are connected with nodes located in neighboring partitions. An internal variable projection subspace is created that is associated with internal variables of the adjacency graph of the matrix system, wherein the internal variables are related to nodes of the adjacency graph which are connected only to nodes located in the same partition. A projection matrix is built based on the interface variable projection subspace and the internal variable projection subspace. The device determines eigenvalues that solve a Raleigh-Ritz eigenvalue problem utilizing the projection matrix.