Helmholtz's equation with a variable wavenumber is solved for a point force through use of a first-order differential equation system approach. Since the system matrix in this formulation is non-constant, an eigensolution is no longer valid and recourse has to be made to approximate techniques ...
A posteriori error estimation for finite element solutions of Helmholtz equation. Part II: estimation of the pollution error. International Journal for Numerical Methods in Engineering 1997; 40:3883-3900.F. Ihlenburg, T. Strouboulis, S.K. Gangaraj, I. Babuska. A posteriori error estimation f...
Helmholtz equation Exp function method Multiple wave solutions Numerical simulation Atmosphere acoustics Full-Text Cite this paper Add to My Lib Abstract: 在线性近似下,Helmholtz方程能够描述小尺度大气声波波动.因此分析小规模大气声波波动特性,必须对Helmholtz方程进行求解.大多数求解Helmholtz方程的方法是在...
Bogy, Novel solutions of the Helmholtz equation and their application to diffraction, Proc. R. Soc. A, 463 (2007) 1005-1027.Budaev, B.V., Bogy, D.B.: Novel solutions of the Helmholtz equation and their application to diffraction. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci...
This paper contains a first systematic analysis of a posteriori estimation for finite element solutions of the Helmholtz equation. In this first part, it is shown that the standard a posteriori estimates, based only on local computations, severely underestimate the exact error for the classes of wa...
Numerical solutions to boundary value problems governed by two-dimensional Helmholtz equation for anisotropic media is obtained. The standard BEM has been employed to obtain the solutions. The results show that the anisotropy of the medium under consideration causes effects on the solution. The ...
Helmholtz equation Wavefields Modeling Neural networks Deep learning 1. Introduction A fundamental part of using surface seismic recorded data to illuminate the Earth is solving the wave equation (Claerbout, 1985). Solving the wave equation numerically constitutes the majority of the computational cost ...
(2021,2023) to prove the nonuniqueness of weak solutions to the transport equation. This scheme was then adapted to the Navier–Stokes equations in Cheskidov and Luo (2022) to prove the sharpness of one of the Prodi–Serrin criteria and in Cheskidov and Luo (2023) to show thatL^2is ...
1. Inverse problems associated with the analysis of exterior boundary value problems for the Helmholtz equation constitute an important part of the inverse scattering theory with major applications...
Use the Gibbs-Helmholtz equation (3.5.3) to derive :Now there is some approximation ( is very small):Finally, we get:Here’s a diagram comparing the precise value and approximate value of the boiling point under different .Depression of Freezing Point: The depression of the freezing point ...