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We examine the problem of solving hyperbolic initial boundary value problems in several space dimensions on parallel computers using domain decomposition. Imposing continuity conditions across an inter-domain boundary in several space dimensions is in general not well posed. If however the boundary moves faster than the fastest wave associated with the hyperbolic equation then the problem becomes well posed. We minimize a function which is the sum of squares of the L2 norm of the residuals in the partial differential equation, initial and boundary conditions and a penalty term which is the...

This book deals with the techniques to solve elliptic eigenvalue problems on polygonal domains using least squares methods. It provides an in-depth treatment of an exponentially accurate nonconforming h-p spectral element method. The spectral element functions are nonconforming and a correction is made to the approximate solution so that the corrected solution is conforming. In this book we discuss the method separately when the boundary of underlying domain is smooth and also when the boundary contains corners. We present error estimates for the eigenvalues and eigenvectors and show that the...