## Advanced Boundary Elements for Heat TransferIn this book the authors present an efficient Boundary Element Method scheme for the numerical solution of two-dimensional heat transfer problems. Lacking the major computational difficulties of traditional reinitialization and convolution schemes, this is of the reinitialization type, in which the domain integrals are computed by a recursive relation that depends only on the boundary temperature and flux at the previous time-step. |

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### Contents

Integral representation formula for heat transfer | 11 |

Nonhistorydependent convolution scheme | 25 |

Recursive reinitialization scheme | 41 |

Copyright | |

7 other sections not shown

### Common terms and phrases

algorithm analysis analytical solution approximation boundary conditions boundary element method boundary value problem Brebbia Chapter collocation point computational considered Convection convolution scheme corresponding CPU-time Crystal Growth degenerate kernel Developments in Heat direct formulation Dirichlet boundary condition domain integral double Fourier series double-layer potential equal evaluate the domain example exponentially fixed boundary Fourier coefficients Fourier series representation free-space fundamental solution given by eqn given in terms Green function Greengard and Strain heat conduction heat equation Heat Exchangers history-dependence initial conditions integral equation integral representation formula interface velocity internal points interpolation functions iterative Jr(t linear Lx Ly melting moving boundary n2k2aAt non-dimensional normal derivative number of terms numerical solution obtained previous time-step reinitialization scheme single-layer and double-layer single-layer potential solidification solved space integrals Strain 15 surface integrals temperature field theorem thermal diffusivity time-step transform trigonometric moments two-dimensional uniform convergence Wrobel