Fourier BEM: Generalization of Boundary Element Methods by Fourier TransformLike FEM, the Boundary Element Method (BEM) provides a general numerical tool for the solution of complex engineering problems. In the last decades, the range of its applications has remarkably been enlarged. Therefore dynamic and nonlinear problems can be tackled. However they still demand an explicit expression of a fundamental solution, which is only known in simple cases. In this respect, the present book proposes an alternative BEM-formulation based on the Fourier transform, which can be applied to almost all cases relevant in engineering mechanics. The basic principle is presented for the heat equation. Applications are taken from solid mechanics (e.g. poroelasticity, thermoelasticity). Transient and stationary examples are given as well as linear and nonlinear. Completed with a mathematical and mechanical glossary, the book will serve as a comprehensive text book linking applied mathematics to real world engineering problems. |
Contents
I | 9 |
III | 10 |
IV | 11 |
V | 15 |
VII | 16 |
VIII | 18 |
IX | 19 |
X | 21 |
XLVII | 85 |
XLVIII | 86 |
XLIX | 87 |
L | 88 |
LI | 91 |
LII | 93 |
LIV | 94 |
LV | 97 |
XI | 23 |
XII | 25 |
XIV | 26 |
XV | 28 |
XVII | 30 |
XVIII | 32 |
XIX | 35 |
XXI | 38 |
XXIII | 39 |
XXIV | 41 |
XXVI | 42 |
XXVII | 43 |
XXVIII | 45 |
XXX | 50 |
XXXI | 55 |
XXXII | 57 |
XXXIII | 58 |
XXXIV | 59 |
XXXV | 61 |
XXXVI | 63 |
XXXVII | 66 |
XXXVIII | 67 |
XXXIX | 68 |
XL | 69 |
XLI | 71 |
XLII | 71 |
XLVI | 83 |
LVI | 98 |
LVII | 100 |
LVIII | 101 |
LIX | 102 |
LX | 103 |
LXI | 104 |
LXII | 105 |
LXIII | 107 |
LXVI | 110 |
LXVII | 111 |
LXX | 112 |
LXXII | 113 |
LXXIV | 117 |
LXXV | 120 |
LXXVI | 123 |
LXXVIII | 125 |
LXXIX | 128 |
LXXX | 132 |
LXXXI | 134 |
LXXXII | 137 |
LXXXIII | 141 |
LXXXIV | 146 |
LXXXV | 151 |
LXXXVI | 159 |
LXXXVIII | 162 |
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Fourier BEM: Generalization of Boundary Element Methods by Fourier Transform Fabian M.E. Duddeck No preview available - 2011 |
Common terms and phrases
algorithm analysis analytical anisotropic arbitrary boundary element method boundary integral equations boundary operator boundary quantities c²x² coefficients collocation constant convolution corner terms cutoff distribution defined derivatives differential equation differential operator Dirac-distribution Dirichlet problem discretization displacements domain dynamic elasticity tensor elements per side Engrg evaluation example F.M.E. Duddeck fast wavelet transform flux Fourier fundamental solution Fourier space Fourier transform free term fundamental solution Galerkin BIE Green's function heat conduction Hence hypersingular î² isotropic isotropic elasticity kernels Kirchhoff leads linear mathematical matrix Mech Meth non-linear normal vector Numer obtained original space orthotropic PhD thesis polynomial right-hand side Rn Rn scalar product scaling functions singular integrals Springer symmetric Galerkin Technische Universität Braunschweig temperature tensor test functions theorem theory thermoelasticity thin plates traction trial and test trial functions u₁ volume forces wavelet transform