PARALLEL NUMERICAL-SOLUTION OF VARIATIONAL-INEQUALITIES

Algorithms which utilize multiprocessing computers are considered for the numerical solution of variational inequalities. Parallel versions of the SOR algorithm with projection to the constraint set are carefully studied. One, analysis assumes the matrix is a symmetric M-matrix and uses multisplitting and upper solutions to deduce convergence of the parallel algorithm. Another analysis uses the constrained minimization characterization of variational inequalities and P-regular multisplittings to obtain convergence. Numerical experiments were done on vector/multiprocessing computers. When using properly ordered multisplitting versions of SOR with projection to the constraint set, substantial speedups of the vector/multiprocessing codes relative to the serial code are observed. Applications to fluid flow in a porous media and to a control problem are examined.