𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Prewavelet approximations for a system of boundary integral equations for plates with free edges on polygons

✍ Scribed by Christian Bourgeois; Serge Nicaise


Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
293 KB
Volume
21
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis


Communicated by E. Meister

We consider the plate equation in a polygonal domain with free edges. Its resolution by boundary integral equations is considered with double layer potentials whose variational formulation was given in Reference 25. We approximate its solution (u, (ju/jn)) by the Galerkin method with approximated spaces made of piecewise polynomials of order 2 and 1 for, respectively, u and (ju/jn). A prewavelet basis of these subspaces is built and equivalences between some Sobolev norms and discrete ones are established in the spirit of References 14, 16, 30 and 31. Further, a compression procedure is presented which reduces the number of nonzero entries of the stiffness matrix from O(N) to O(N log N), where N is the size of this matrix. We finally show that the compressed stiffness matrices have a condition number uniformly bounded with respect to N and that the compressed Galerkin scheme converges with the same rate than the Galerkin one. 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.