Weighting the recursive spectral bisection algorithm for unstructured grids

TL;DR: When solving partial differential equations numerically on parallel computers it is desirable to decompose the domain on which the authors are solving the equations in such a way as to equalize the workload among the processors while minimizing the communication between them.

Abstract: When solving partial differential equations numerically on parallel computers it is desirable to decompose the domain on which we are solving the equations in such a way as to equalize the workload among the processors while minimizing the communication between them. This is equivalent to finding a partition of the graph representing the calculation into equal subgraphs cutting as few edges as possible. One such algorithm in use is the recursive spectral bisection algorithm (RSB), (1) generate the Laplace matrix for the graph representing the dependencies between the calculation taking place at each vertex of the graph. (2) Compute the eigenvector corresponding to the smallest non-zero eigen-value, called the Fiedler vector. (3) Sort the vertices according to size of entries in the Fiedler vector. (4) Assign half the vertices into each subgraph.