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 careful ly studied. One, analysis assumes the matrix is a symmetric M-matrix a nd uses multisplitting and upper solutions to deduce convergence of th e parallel algorithm. Another analysis uses the constrained minimizati on characterization of variational inequalities and P-regular multispl ittings to obtain convergence. Numerical experiments were done on vect or/multiprocessing computers. When using properly ordered multisplitti ng versions of SOR with projection to the constraint set, substantial speedups of the vector/multiprocessing codes relative to the serial co de are observed. Applications to fluid flow in a porous media and to a control problem are examined.