Pulsating Spectral Element Methods for Hyperbolic Problems: Hyperbolic Problems and Domain Decomposition Method - Softcover

Lamba, Subir; Dutt, Pravir

Softcover

ISBN 10: 3639325184 ISBN 13: 9783639325188

Publisher: VDM Verlag Dr. Müller, 2011

Synopsis

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 sum of squares of the L2 norm of the jumps in the function across inter-domain boundaries. The inter-domain boundaries are made to move back and forth at alternate time steps with sufficiently high speed to make the problem well posed. The alternating Schwarz waveform Relaxation technique experiences difficulties if the characteristics change sign at inter-element boundaries or even in the interior of the domains. We use the spectral element method to obtain the numerical solution of the problem. The normal equations are solved by Preconditioned Conjugate Gradient Method (PCGM).

About this title

About the Author

A native of Lucknow, the author did his graduation and post graduation from Lucknow university. Then he joined the Ph.D program at IIT Kanpur in 1998. This book is doctoral thesis of his work at IIT Kanpur under the supervision of Prof. Pravir Dutt.

Edition details

• Publisher: VDM Verlag Dr. Müller
• Publication date: 2011
• Language: English
• ISBN 10: 3639325184
• ISBN 13: 9783639325188
• Binding: Paperback
• Number of pages: 108