Advanced boundary elements for heat transfer Machine generated contents note: Chapter 1 Introduction 1.1 Related schemes 1.2 Contents of this work Chapter 2 Integral representation formula for heat transfer 2.1 Introduction 2.2 Integral representation formula 2.3 Boundary element method Chapter 3 Non history dependent convolution scheme 3.1 Introduction 3.2 Green function 3.3 Integral equation with degenerate kemal 3.4 Convolution scheme Chapter 4 Recursive reinitialization scheme 4.1 Introduction 4.2 Greengard and Strain algorithm 4.3 Boundary integral equation 4.4 Proposed numerical scheme 4.5 Internal value of the temperature using Fourier series Chapter 5 Numerical examples for fixed boundaries 5.1 Numerical results 5.1.1 Accuracy comparison 5.2 CPU time comparison 5.3 Refined approach by adding images Chapter 6 Thermal diffusion with moving boundary 6.1 Introduction 6.2 Boundary integral representation 6.3 Proposed numerical scheme Chapter 7 Numerical examples with moving boundary 7.1 Introduction 7.2 Numerical examples Appendices Appendix A Fourier series representation for the Green function Appendix B Bounds for the integral of the absolute value of the kernal and for the truncated Fourier series in the convolution scheme Appendix C Truncation error bound for the Fourier series Appendix D Surface trigonometric moments of u and q Appendix E Analytical space integration of the single layer potential when the collocation point lies in the integration element References