All Project

examples/gmsh_api/my_geo.geo

+Lx = 5;
+Ly = 2;
+nx = 5;
+ny = 1;
+
+Point(1) = {0, 0, 0, 1.0};
+Point(2) = {Lx, 0, 0, 1.0};
+Point(3) = {Lx, Ly, 0, 1.0};
+Point(4) = {0, Ly, 0, 1.0};
+Line(1) = {1, 2};
+Line(2) = {2, 3};
+Line(3) = {3, 4};
+Line(4) = {4, 1};
+Curve Loop(1) = {4, 1, 2, 3};
+Plane Surface(1) = {1};
+Transfinite Curve {3, 1} = nx+1 Using Progression 1;
+Transfinite Curve {4, 2} = ny+1 Using Progression 1;
+Transfinite Surface {1};
+
+Recombine Surface {1}; // quads instead of triangles
+
+Physical Curve("left_edge", 5) = {4};
+Physical Surface("domain", 6) = {1};
+Physical Curve("top_edge",7) = {3};
+
+// additional parameters given to the solver
+SetNumber("Boundary Conditions/left_edge/ux", 0.);
+SetNumber("Boundary Conditions/left_edge/uy", 0.);
+SetNumber("Materials/domain/Young", 210e3);
+SetNumber("Materials/domain/Poisson", 0.3);
+SetNumber("Boundary Conditions/top_edge/tx", 0.);
+SetNumber("Boundary Conditions/top_edge/ty", -100.);
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examples/gmsh_api/rectangle.geo

+Lx = 10;
+Ly = 2;
+nx = 5;
+ny = 1;
+
+Point(1) = {0, 0, 0, 1.0};
+Point(2) = {Lx, 0, 0, 1.0};
+Point(3) = {Lx, Ly, 0, 1.0};
+Point(4) = {0, Ly, 0, 1.0};
+Line(1) = {1, 2};
+Line(2) = {2, 3};
+Line(3) = {3, 4};
+Line(4) = {4, 1};
+Curve Loop(1) = {4, 1, 2, 3};
+Plane Surface(1) = {1};
+Transfinite Curve {3, 1} = nx+1 Using Progression 1;
+Transfinite Curve {4, 2} = ny+1 Using Progression 1;
+Transfinite Surface {1};
+
+Recombine Surface {1}; // quads instead of triangles
+
+Physical Curve("left_edge", 5) = {4};
+Physical Surface("domain", 6) = {1};
+Physical Curve("top_edge",7) = {3};
+
+// additional parameters given to the solver
+SetNumber("Boundary Conditions/left_edge/ux", 0.);
+SetNumber("Boundary Conditions/left_edge/uy", 0.5);
+SetNumber("Materials/domain/Young", 210e3);
+SetNumber("Materials/domain/Poisson", 0.3);
+SetNumber("Boundary Conditions/top_edge/tx", 0.);
+SetNumber("Boundary Conditions/top_edge/ty", -100.);
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examples/sparse_solve/CMakeLists.txt

+PROJECT(SPARSE_SOLVE CXX)
+CMAKE_MINIMUM_REQUIRED(VERSION 3.12)
+
+# ------------------------------------------------------------------------------
+# Find libraries and setup compiler
+# ------------------------------------------------------------------------------
+
+# build type is "" by default in Linux
+IF(NOT CMAKE_BUILD_TYPE)
+    SET( CMAKE_BUILD_TYPE "Release" CACHE STRING "" FORCE)
+ENDIF()
+
+# enable C++11
+SET(CMAKE_CXX_STANDARD 11)
+SET(CMAKE_CXX_STANDARD_REQUIRED ON)
+
+IF(APPLE)
+    # on macOS, do not give priority to frameworks/apps
+    SET(CMAKE_FIND_APPBUNDLE LAST)
+    SET(CMAKE_FIND_FRAMEWORK LAST)
+ENDIF()
+
+# find gmsh-sdk
+# gmsh.h
+FIND_PATH(GMSH_INCLUDE_DIRS NAMES "gmsh.h")
+MESSAGE(STATUS "GMSH_INCLUDE_DIRS=" ${GMSH_INCLUDE_DIRS})
+if(NOT GMSH_INCLUDE_DIRS)
+    MESSAGE(FATAL_ERROR "gmsh.h not found!")
+ENDIF()
+INCLUDE_DIRECTORIES(${GMSH_INCLUDE_DIRS})
+
+# libgmsh.so
+FIND_LIBRARY(GMSH_LIBRARIES gmsh)
+MESSAGE(STATUS "GMSH_LIBRARIES=" ${GMSH_LIBRARIES})
+IF(NOT GMSH_LIBRARIES)
+    MESSAGE(FATAL_ERROR "gmsh library not found!")
+ENDIF()
+
+# find Eigen
+find_path(EIGEN_INCLUDE_DIRS "Eigen/Dense" 
+          PATHS "${PROJECT_SOURCE_DIR}/lib/eigen" "/usr/include/eigen3")
+MESSAGE(STATUS "EIGEN_INCLUDE_DIRS=" ${EIGEN_INCLUDE_DIRS})
+IF(NOT EIGEN_INCLUDE_DIRS)
+    MESSAGE(FATAL_ERROR "Eigen include dir not found!")
+ENDIF()
+INCLUDE_DIRECTORIES(${EIGEN_INCLUDE_DIRS})
+
+# ------------------------------------------------------------------------------
+
+SET(SRCS Tutorial_sparse_example.cpp Tutorial_sparse_example_details.cpp)
+ADD_EXECUTABLE(solve_sparse ${SRCS})
+TARGET_LINK_LIBRARIES(solve_sparse ${GMSH_LIBRARIES})

examples/sparse_solve/README.md

+# sparse_solve
+
+This program solves a sparse linear system with Eigen. 
+
+The files are directly taken from the Eigen source tree and put here without any modification.

examples/sparse_solve/Tutorial_sparse_example.cpp

+#include <Eigen/Sparse>
+#include <vector>
+#include <iostream>
+
+typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
+typedef Eigen::Triplet<double> T;
+
+void buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n);
+void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename);
+
+int main(int argc, char** argv)
+{
+  // if(argc!=2) {
+  //   std::cerr << "Error: expected one and only one argument.\n";
+  //   return -1;
+  // }
+  
+  int n = 300;  // size of the image
+  int m = n*n;  // number of unknows (=number of pixels)
+
+  // Assembly:
+  std::vector<T> coefficients;            // list of non-zeros coefficients
+  Eigen::VectorXd b(m);                   // the right hand side-vector resulting from the constraints
+  buildProblem(coefficients, b, n);
+
+  SpMat A(m,m);
+  A.setFromTriplets(coefficients.begin(), coefficients.end());
+
+  // Solving:
+  Eigen::SimplicialCholesky<SpMat> chol(A);  // performs a Cholesky factorization of A
+  Eigen::VectorXd x = chol.solve(b);         // use the factorization to solve for the given right hand side
+
+  // Export the result to a file:
+  // saveAsBitmap(x, n, argv[1]);
+
+  return 0;
+}
+

examples/sparse_solve/Tutorial_sparse_example_details.cpp

+#include <Eigen/Sparse>
+#include <vector>
+// #include <QImage>
+
+typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
+typedef Eigen::Triplet<double> T;
+
+void insertCoefficient(int id, int i, int j, double w, std::vector<T>& coeffs,
+                       Eigen::VectorXd& b, const Eigen::VectorXd& boundary)
+{
+  int n = int(boundary.size());
+  int id1 = i+j*n;
+
+        if(i==-1 || i==n) b(id) -= w * boundary(j); // constrained coefficient
+  else  if(j==-1 || j==n) b(id) -= w * boundary(i); // constrained coefficient
+  else  coeffs.push_back(T(id,id1,w));              // unknown coefficient
+}
+
+void buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n)
+{
+  b.setZero();
+  Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0,M_PI).sin().pow(2);
+  for(int j=0; j<n; ++j)
+  {
+    for(int i=0; i<n; ++i)
+    {
+      int id = i+j*n;
+      insertCoefficient(id, i-1,j, -1, coefficients, b, boundary);
+      insertCoefficient(id, i+1,j, -1, coefficients, b, boundary);
+      insertCoefficient(id, i,j-1, -1, coefficients, b, boundary);
+      insertCoefficient(id, i,j+1, -1, coefficients, b, boundary);
+      insertCoefficient(id, i,j,    4, coefficients, b, boundary);
+    }
+  }
+}
+
+// void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename)
+// {
+//   Eigen::Array<unsigned char,Eigen::Dynamic,Eigen::Dynamic> bits = (x*255).cast<unsigned char>();
+//   QImage img(bits.data(), n,n,QImage::Format_Indexed8);
+//   img.setColorCount(256);
+//   for(int i=0;i<256;i++) img.setColor(i,qRgb(i,i,i));
+//   img.save(filename);
+// }

lib/README.md

+# math0471/lib
+
+This folder contains scripts for downloading the 2 external libraries that are required for this project.
\ No newline at end of file

lib/get_eigen.cmd

+::@echo off
+:: download eigen & extract to current folder
+
+set version=3.4.0
+set file=eigen-%version%.zip
+
+:: download file
+del %file%  >nul 2>&1
+bitsadmin /transfer get_eigen /dynamic /download /priority foreground "https://gitlab.com/libeigen/eigen/-/archive/%version%/%file%" "%CD%\%file%"
+
+:: unzip
+rd /Q/S eigen-%version%  >nul 2>&1
+powershell.exe -nologo -noprofile -command "& { Add-Type -A 'System.IO.Compression.FileSystem'; [IO.Compression.ZipFile]::ExtractToDirectory('%CD%\%file%', '%CD%'); }"
+del %file%  >nul 2>&1
+
+:: rename folder
+rd /Q/S eigen >nul 2>&1
+ren eigen-%version% eigen

lib/get_eigen.sh

+#!/bin/bash
+
+set -e
+
+VERSION=3.4.0
+
+wget -q https://gitlab.com/libeigen/eigen/-/archive/${VERSION}/eigen-${VERSION}.tar.gz
+tar xzf eigen-${VERSION}.tar.gz
+rm eigen-${VERSION}.tar.gz
+rm -rf eigen
+mv eigen-${VERSION} eigen

lib/get_gmsh.cmd

+::@echo off
+:: download gmsh-sdk & extract to current folder
+
+set gmsh=gmsh-4.9.3-Windows64-sdk
+set file=%gmsh%.zip
+
+:: download file
+del %file%  >nul 2>&1
+bitsadmin /transfer get_gmsh /dynamic /download /priority foreground "https://gmsh.info/bin/Windows/%file%" "%CD%\%file%"
+
+:: unzip
+rd /Q/S %gmsh%  >nul 2>&1
+powershell.exe -nologo -noprofile -command "& { Add-Type -A 'System.IO.Compression.FileSystem'; [IO.Compression.ZipFile]::ExtractToDirectory('%CD%\%file%', '%CD%'); }"
+del %file%  >nul 2>&1
+
+:: rename folder
+rd /Q/S gmsh-sdk >nul 2>&1
+ren %gmsh% gmsh-sdk
+
+:: copy dll to bin folder so that double-clic on gmsh.exe works!
+copy /Y gmsh-sdk\lib\gmsh-*.dll gmsh-sdk\bin\

lib/get_gmsh.sh

+#!/bin/bash
+
+set -e
+
+VERSION=4.9.3
+
+if [[ "$OSTYPE" == "linux-gnu" ]]; then
+    wget -q https://gmsh.info/bin/Linux/gmsh-${VERSION}-Linux64-sdk.tgz
+    tar xzf gmsh-${VERSION}-Linux64-sdk.tgz
+    rm gmsh-${VERSION}-Linux64-sdk.tgz
+    rm -rf gmsh-sdk
+    mv gmsh-${VERSION}-Linux64-sdk gmsh-sdk
+elif [[ "$OSTYPE" == "darwin"* ]]; then
+    wget -q https://gmsh.info/bin/MacOSX/gmsh-${VERSION}-MacOSX-sdk.tgz
+    tar xzf gmsh-${VERSION}-MacOSX-sdk.tgz
+    rm gmsh-${VERSION}-MacOSX-sdk.tgz
+    rm -rf gmsh-sdk
+    mv gmsh-${VERSION}-MacOSX-sdk gmsh-sdk
+else
+    echo "unknown system"
+fi

srcs/CMakeLists.txt

+PROJECT(MATH0471 CXX)
+CMAKE_MINIMUM_REQUIRED(VERSION 3.12)
+
+# ------------------------------------------------------------------------------
+# Find libraries and setup compiler
+# ------------------------------------------------------------------------------
+
+# build type is "" by default in Linux
+IF(NOT CMAKE_BUILD_TYPE)
+    SET( CMAKE_BUILD_TYPE "Release" CACHE STRING "" FORCE)
+ENDIF()
+
+# enable C++11
+SET(CMAKE_CXX_STANDARD 11)
+SET(CMAKE_CXX_STANDARD_REQUIRED ON)
+
+IF(APPLE)
+    # on macOS, do not give priority to frameworks/apps
+    SET(CMAKE_FIND_APPBUNDLE LAST)
+    SET(CMAKE_FIND_FRAMEWORK LAST)
+ENDIF()
+
+# find gmsh-sdk
+# gmsh.h
+FIND_PATH(GMSH_INCLUDE_DIRS NAMES "gmsh.h")
+MESSAGE(STATUS "GMSH_INCLUDE_DIRS=" ${GMSH_INCLUDE_DIRS})
+if(NOT GMSH_INCLUDE_DIRS)
+    MESSAGE(FATAL_ERROR "gmsh.h not found!")
+ENDIF()
+INCLUDE_DIRECTORIES(${GMSH_INCLUDE_DIRS})
+
+# libgmsh.so
+FIND_LIBRARY(GMSH_LIBRARIES gmsh)
+MESSAGE(STATUS "GMSH_LIBRARIES=" ${GMSH_LIBRARIES})
+IF(NOT GMSH_LIBRARIES)
+    MESSAGE(FATAL_ERROR "gmsh library not found!")
+ENDIF()
+
+# find Eigen
+find_path(EIGEN_INCLUDE_DIRS "Eigen/Dense" 
+          PATHS "${PROJECT_SOURCE_DIR}/lib/eigen" "/usr/include/eigen3")
+MESSAGE(STATUS "EIGEN_INCLUDE_DIRS=" ${EIGEN_INCLUDE_DIRS})
+IF(NOT EIGEN_INCLUDE_DIRS)
+    MESSAGE(FATAL_ERROR "Eigen include dir not found!")
+ENDIF()
+INCLUDE_DIRECTORIES(${EIGEN_INCLUDE_DIRS})
+
+# ------------------------------------------------------------------------------
+
+FILE(GLOB SRCS *.cpp)
+ADD_EXECUTABLE(solver ${SRCS})
+TARGET_LINK_LIBRARIES(solver ${GMSH_LIBRARIES})

srcs/README.md

+# srcs
+
+You can start your project here.

srcs/main.cpp

+#include <iostream>
+
+int main(int argc, char **argv)
+{
+    std::cout << "Hello world!\n";
+
+    return 0;
+}
\ No newline at end of file