A variable order wavelet method for the sparse representation of layer potentials in the non-standard form.
J Tausch - Journal of Numerical Mathematics, 2004 - degruyter.com
Journal of Numerical Mathematics, 2004•degruyter.com
We discuss a variable order wavelet method for boundary integral formulations of elliptic
boundary value problems. The wavelet basis functions are transformations of standard
nodal basis functions and have a variable number of vanishing moments. For integral
equations of the second kind we will show that the non-standard form can be compressed to
contain only O (N) non-vanishing entries while retaining the asymptotic converge of the full
Galerkin scheme, where N is the number of degrees of freedom in the discretization.
boundary value problems. The wavelet basis functions are transformations of standard
nodal basis functions and have a variable number of vanishing moments. For integral
equations of the second kind we will show that the non-standard form can be compressed to
contain only O (N) non-vanishing entries while retaining the asymptotic converge of the full
Galerkin scheme, where N is the number of degrees of freedom in the discretization.
Abstract
We discuss a variable order wavelet method for boundary integral formulations of elliptic boundary value problems. The wavelet basis functions are transformations of standard nodal basis functions and have a variable number of vanishing moments. For integral equations of the second kind we will show that the non-standard form can be compressed to contain only O (N) non-vanishing entries while retaining the asymptotic converge of the full Galerkin scheme, where N is the number of degrees of freedom in the discretization.
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