Galerkin FEM for elliptic PDEs
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  1. %\documentclass[11pt]{article}
  2. %\documentclass[a4paper,11pt]{report}
  3. %\documentclass[11pt]{report}
  4. %\documentclass[a4paper,11pt]{scrartcl}
  5. \documentclass[a4paper,11pt]{scrreprt} %book}
  6. %\usepackage{times}
  7. \usepackage{fullpage,amsmath,placeins,graphicx,color,amssymb,setspace,listings,tikz,amsthm,yfonts,subfigure}
  8. \usepackage{natbib}
  9. \usepackage[linkbordercolor=white,citecolor={1 1 1}]{hyperref}
  10. \usepackage{amsthm} % theorem
  11. \newcounter{proof}
  12. \stepcounter{proof}
  13. \newtheorem{corollary}{Corollary}[proof]
  14. \definecolor{dkgreen}{rgb}{0,0.6,0}
  15. \definecolor{gray}{rgb}{0.5,0.5,0.5}
  16. %\lstset{language=c++,numbers=left,numberstyle=\tiny,showstringspaces=false,color=true}
  17. \lstset{language=c++,
  18. keywords={real, VectorXd, SparseMatrix, string, this, default, exit, float, double,int, break, case,
  19. catch,continue,else,elseif,end,for,function,Real,Complex,
  20. global,if,otherwise,persistent,return,switch,try,while,long, unsigned, vector},
  21. basicstyle=\ttfamily,
  22. keywordstyle=\color{blue},
  23. commentstyle=\color{red},
  24. stringstyle=\color{dkgreen},
  25. numbers=left,
  26. numberstyle=\tiny\color{gray},
  27. stepnumber=1,
  28. numbersep=10pt,
  29. backgroundcolor=\color{white},
  30. tabsize=4,
  31. showspaces=false,
  32. showstringspaces=false}
  33. \def\LAPL#1{\nabla^2 {#1}}
  34. \def\VEC#1{\mathbf{#1}}
  35. \def\LBM{ \mathcal{L} ( \mathbb{R}^n ) }
  36. \def\LBO{ \mathcal{L} ( \mathbb{R}^1 ) }
  37. \def\LBT{ \mathcal{L} ( \mathbb{R}^2 ) }
  38. \def\REB{ \mathbb{R} }
  39. \def\REBN{ \mathbb{R}^n }
  40. \def\CENSECA{\alpha(U_{n+1}^m-2U_n^m+U_{n-1}^m)}
  41. %\def\DD#1{\frac{\partial}{\partial #1}}
  42. \def\DD#1{\frac{d}{d #1}}
  43. \author{Trevor Irons \\
  44. XRI Geophysics, LLC \\
  45. Trevor.Irons@xrigeo.com }
  46. \title{FEM4EllipticPDE}
  47. \subtitle{Lemma module v1.0}
  48. \begin{document}
  49. \maketitle
  50. \tableofcontents
  51. \renewcommand{\labelenumi}{(\Roman{enumi})}
  52. \renewcommand{\labelenumii}{(\arabic{enumii})}
  53. \renewcommand{\labelenumiii}{(\roman{enumiii})}
  54. \abstract
  55. This Lemma module provides a Galerkin-style finite element solution to general elliptic problems.
  56. Lemma is an open source geophysical programming API that supports modular plug-ins, such as this one.
  57. Lemma may be freely downloaded from \href{http://lemmasoftware.org}{http://lemmasoftware.org}.
  58. This module is currently closed source. Development of FEM4EllipticPDE started at the
  59. Center for Gravity Electrical and Magnetic Studies (CGEM) at the Colorado School of Mines. The modules
  60. was completed by XRI Geophysics, LLC.
  61. \input{chapters/derivation}
  62. \input{chapters/usage}
  63. \input{chapters/magnetics}
  64. \input{chapters/examples}
  65. \bibliographystyle{seg}
  66. \bibliography{nmr}
  67. \end{document}