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Arbitrarily High-Order Convergence of Wavelet-based Galerkin Scheme for 1D Elliptic Interface Problems
Bin Han, Michelle Michelle
The solution of an elliptic interface problem in a domain is often smooth away from the interface , but its gradient is discontinuous across . Consequently,…
High-order, Compact, and Symmetric Finite Difference Methods for -Dimensional Elliptic Equations
Qiwei Feng, Bin Han, Michelle Michelle +1
This paper presents compact, symmetric, and high-order finite difference methods (FDMs) for the variable Poisson equation on a -dimensional hypercube. Our schemes produce symmet…
Galerkin Scheme Using Biorthogonal Wavelets on Intervals for Elliptic Interface Problems
Bin Han, Michelle Michelle
This paper presents a wavelet Galerkin method for solving elliptic interface problems of the form in , where is a smooth interface wi…
Wavelets on Intervals Derived from Arbitrary Compactly Supported Biorthogonal Multiwavelets
Bin Han, Michelle Michelle
(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems in applications are defined on bounded in…
Dirac Assisted Tree Method for 1D Heterogeneous Helmholtz Equations with Arbitrary Variable Wave Numbers
Bin Han, Michelle Michelle, Yau Shu Wong
In this paper we introduce a new method called the Dirac Assisted Tree (DAT) method, which can handle 1D heterogeneous Helmholtz equations with arbitrarily large variable wave numb…
Wavelet-based Methods for Numerical Solutions of Differential Equations
Bin Han, Michelle Michelle, Yau Shu Wong
Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tre…