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math.NA2026
Explicit Runge approximation for Helmholtz equation with cylindrical harmonics
Yu Chen, Jin Cheng, Tingyue Li
Originating from the complex approximation of holomorphic functions, the Runge approximation for elliptic equations has evolved into a fundamental tool for inverse problems and eve…
math.NA2024★ 1 cited
Learning based numerical methods for Helmholtz equation with high frequency
Yu Chen, Jin Cheng, Tingyue Li +1
High-frequency issues have been remarkably challenges in numerical methods for partial differential equations. In this paper, a learning based numerical method (LbNM) is proposed f…
math.NA2023
Harmonic Measures and Numerical Computation of Cauchy Problems for Laplace Equations
Yu Chen, Jin Cheng, Shuai Lu +1
It is well known that Cauchy problem for Laplace equations is an ill-posed problem in Hadamard's sense. Small deviations in Cauchy data may lead to large errors in the solutions. I…