Parallel Algorithms for the Solution of the Schrodinger Equation

Many of the traditional numerical algorithms do not map easily onto the architecture of parallel computers that have emerged recently. For the economic use of these expensive machines and to reduce the total computing time, it is necessary to develop efficient parallel algorithms. The purpose of the thesis is to develop several parallel algorithms for the numerical solution of the Schrodinger equation which arises in many branches of atomic and molecular physics. Common models of systems which are of interest may represent stable configurations of two particles, the bound state or eigenvalue problem. Alternately one may consider either singlechannel or multi-channel scattering. All three mathematical models will be investigated in this work. Emphasis is placed on parallel algorithms for MIMD machines. All the algorithms have been implemented and tested on a transputer network which is a MIMD machine without shared memory. Existing numerical methods such as those ascribed to Numerov and De Vogelaere have been investigated and parallel versions of them have been developed. Two exponentially fitted versions of the De Vogelacre algorithm have been developed and they are found to be more efficient than the normal De Vogelaere algorithm