Boundary Integral Solutions of the Heat Equation

McIntyre, Jr. E A

doi:10.2307/2008215

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Cited by 5 publications

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A fast algorithm for the evaluation of heat potentials

Greengard

Strain

1990

Comm Pure Appl Math

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Numerical methods for solving the heat equation via potential theory have been hampered by the high cost of evaluating heat potentials. When M points are used in the discretization of the boundary and N time steps are computed, an amount of work of the order O(N2M2) has traditionally been required. In this paper, we present an algorithm which requires an amount of work of the order O(NM), and we observe speedups of five orders of magnitude for large‐scale problems. Thus, the method makes it possible to solve the heat equation by potential theory in practical situations.

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A fast algorithm for the evaluation of heat potentials

Greengard

Strain

1990

Comm Pure Appl Math

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Boundary Conditions for Viscous Vortex Methods

Koumoutsakos

Leonard

Pepin

1994

Journal of Computational Physics

133

125

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Modelling the motion of clusters of cells in a viscous fluid using the boundary integral method

Harris

2018

Mathematical Biosciences

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In experiments clusters of cells are often observed to move in response to a chemical signal which is present in the fluid surrounding the cells. This process is known as chemotaxis. This paper presents a method for modelling the motion of clusters of cells moving through a viscous fluid in response to a known chemical signal using a boundary integral formulation of the governing equations rather than the more usual differential equation formulation. The numerical results presented in this paper show that the boundary integral method can be used to simulate the motion of cell clusters through the fluid. The results of the simulations are compared to some experimental observations of cell and cluster motion.

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Boundary Integral Solutions of the Heat Equation

Abstract: Abstract. The Boundary Integral Method (BIM) has recently become quite popular because of its ability to provide cheap numerical solutions to the Laplace equation. This paper describes an attempt to apply a similar approach to the (time-dependent) heat equation in two space variables.

Cited by 5 publications

References 11 publications

A fast algorithm for the evaluation of heat potentials

A fast algorithm for the evaluation of heat potentials

Boundary Conditions for Viscous Vortex Methods

Modelling the motion of clusters of cells in a viscous fluid using the boundary integral method

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