4 papers
An improvement on B-spline basis condition number
Yimin Zhong
In this short note, we improve the upper bound on the condition number of the univariate B-spline basis of order from to for all .
From Frequency Bias to Spectral Balance: Operator-Aware Preconditioners for PINNs
Roy Y. He, Ying Liang, Hongkai Zhao +1
When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning…
Forward and inverse problems of a semilinear transport equation
Kui Ren, Yimin Zhong
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our firs…
Error Analysis for the Implicit Boundary Integral Method
Yimin Zhong, Kui Ren, Olof Runborg +1
The implicit boundary integral method (IBIM) provides a framework to construct quadrature rules on regular lattices for integrals over irregular domain boundaries. This work provid…