Wave-heat coupling in one-dimensional unbounded domains: artificial boundary conditions and an optimized Schwarz method

The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. In this paper, we consider the construction of artificial boundary conditions (ABCs) for semi-discretized peridynamics using Green functions. Especially, the Green functions that represent the response to the single wave source are used to construct the accu2rate boundary conditions. The recursive relationships between the Green functions are proposed, therefore the Green functions can be computed through a differential and integral system with high precision. The numerical results demonstrate the accuracy of the proposed ABCs. The proposed method can be applied to modelling of wave propagation for other non-local theories and high-dimensional cases.

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A class of artificial boundary conditions for heat equation in unbounded domains

Computers & Mathematics with Applications ◽

10.1016/s0898-1221(01)00329-7 ◽

2002 ◽

Vol 43 (6-7) ◽

pp. 889-900 ◽

Cited By ~ 44

Author(s):

Houde Han ◽

Zhongyi Huang

Keyword(s):

Boundary Conditions ◽

Heat Equation ◽

Unbounded Domains ◽

Artificial Boundary ◽

Artificial Boundary Conditions

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Artificial boundary conditions for numerical modeling of electron oscillations in plasma

Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie) ◽

10.26089/nummet.v18r106 ◽

2017 ◽

pp. 65-79

Author(s):

Е.В. Чижонков

Keyword(s):

Boundary Conditions ◽

Numerical Experiments ◽

Asymptotic Methods ◽

Electron Plasma ◽

Dimensional Electron ◽

Artificial Boundary ◽

Plasma Oscillations ◽

Breaking Effect ◽

One Dimensional ◽

Artificial Boundary Conditions

Асимптотическими методами изучается поведение функций, описывающих релятивистский эффект опрокидывания плоских одномерных электронных плазменных колебаний. Полученные формулы порождают различные виды искусственных граничных условий, которые анализируются с помощью численных экспериментов. Специально подобранная комбинация предложенных граничных условий используется для моделирования эффекта опрокидывания в пространственно двумерном случае. Часть расчетов была проведена на СКИФ МГУ "Чебышев" (МГУ им. М.В. Ломоносова). The behavior of the functions describing the relativistic breaking effect of plane one-dimensional electron plasma oscillations is studied by asymptotic methods. The obtained formulas generate various forms of artificial boundary conditions which analyzed by numerical experiments. A special combination of the proposed boundary conditions is used to simulate the breaking effect in the spatially two-dimensional case. A part of computation was performed on the "Chebyshev" Moscow University supercomputer system.

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