13 citations · 26 across the 10 of their papers we have counts for
10 papers
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,…
Convergent Compact Finite Difference Methods with Symmetric Matrices and Highest Possible Orders for Variable-Coefficient Elliptic Equations
Qiwei Feng, Bin Han, Michelle Michelle +1
For the -dimensional variable-coefficient Poisson problem subject to Dirichlet boundary conditions, we seek compact (i.e., -point) symmetric fi…
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…
Optimal Neural Network Approximation for High-Dimensional Continuous Functions
Ayan Maiti, Michelle Michelle, Haizhao Yang
Recently, the authors of \cite{SYZ22} developed a neural network with width and depth , which utilizes a special activation function called the elementary univers…
Wavelet Galerkin Method for an Electromagnetic Scattering Problem
Bin Han, Michelle Michelle
The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In th…
Sixth Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect
Qiwei Feng, Bin Han, Michelle Michelle
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the recip…
Sharp Stability Wavenumber-explicit Bounds for 2D Helmholtz Equations
Bin Han, Michelle Michelle
Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very f…
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…