Bi-orthonormal wavelets and numerical boundary measures for wavelet-Galerkin methods
Abstract
The primary objective of this research is to study the application of B-spline wavelets in the approximation of the solutions of differential equations. The multiscale representation of geometric domains and their boundaries using B-splines is demonstrated. These are useful for specific numerical calculations in which boundary conditions are enforced over arbitrary domains using the penalty method. The formulation and solution of a multiscale wavelet-Galerkin problem using the penalty method is derived and the error in the solution is shown to depend on the order of the B-spline as well as the resolution level. The use of wavelets in multigridding strategies is demonstrated and the accuracy of the resulting solution is shown to be enhanced. The a posteriori error estimates, as presented by Bank and Smith [Ref 2], are validated and shown to be good error indicators. They are used to determine and compare the errors for solutions on different subspaces for wavelet Galerkin methods.
Description
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Includes bibliographical references.
Includes bibliographical references.
Keywords
aerospace engineering., Major aerospace engineering.