Mathematical Programming Approach for Static Load Balancing of Parallel Pde Solver

A static load-balancing scheme is discussed for numerical simulation system NSL, which automatically generates parallel solver of partial differential equations, PDE, from high level description of problem. NSL partitions computational domain into multiple blocks, and allocates processors optimally for each block in accordance with computation and communication cost. This allocation problem is formulated as a combinatorial optimization problem, and solved by branch-and-bound method. Though it is impractical to solve large problems by this method because of combinatorial explosion, this paper also describes an effective method to derive suboptimal solution in practical time by limiting search space. The error of this approximation is less than 15% under reasonable condition. Elapsed time for combinatorial optimization is measured in numerical simulations to induce the estimation equation. The method presented here is widely applicable by adapting evaluation function for each purpose.