A Parallel, Object-Oriented Implementation of the Dynamic Recursion Method

We present the rst parallel, object-oriented C++ implementation of the dynamic recursion method. The recursion method is a means to tridiagonalize sparse matrices eeciently and is useful for a wide number of problems in physics. Dynamic recursion describes an optimization of the standard recursion method by operating only with a dynamically varying subset of basis vectors|reducing memory needs and allowing the computation of very large systems. We show how a graph-based data structure permits storing and multiplying sparse matrices and vectors eeciently. We use a tree structure to cope with the dynamically changing basis set, manifested by perpetual creation and elimination of vector components and matrix elements. A \workpile" approach is employed to allow thread-based parallel execution. Systems with up to 10 7 matrix elements have been simulated with the current implementation and the Anderson metal-insulator transition has been studied as a test-bed project.