Switch to periodic boundary conditions

simucene/glut_grapher.cpp

@@ -78,7 +78,7 @@ void GlutGrapher::display() const {
 
 //..................................................................................................
 void GlutGrapher::idle() {
-    bool const wait_to_start = true;
+    bool const wait_to_start = false;
     if (wait_to_start && frame_ == 0) {
         std::cout << "Press enter to start a 5 second countdown" << std::endl;
         do {} while (std::cin.get() != '\n');

simucene/main.cpp

@@ -12,12 +12,18 @@ void mouse(int, int, int, int) { exit(0); }
 
 //--------------------------------------------------------------------------------------------------
 SparseMatrix<Scalar> d_x_first_order(int32_t const dim) {
-    return MatrixBuilder(dim).stripe(0, -1).stripe(1, 1);
+    // stripe(0, -1) means add a stripe of -1s on the diagonal
+    // stripe(1, 1) means add a stripe of 1s one above the diagonal
+    // element(dim - 1, 0, 1) means add a single 1 at row dim - 1 and column 0
+    return MatrixBuilder(dim).stripe(0, -1).stripe(1, 1).element(dim - 1, 0, 1);
 }
 
 //--------------------------------------------------------------------------------------------------
 SparseMatrix<Scalar> d_x2_first_order(int32_t const dim) {
-    return MatrixBuilder(dim).stripe(-1, 1).stripe(0, -2).stripe(1, 1);
+    return MatrixBuilder(dim)
+        .stripe(-1, 1).element(0, dim - 1, 1)
+        .stripe(0, -2)
+        .stripe(1, 1).element(dim - 1, 0, 1);
 }
 
 //--------------------------------------------------------------------------------------------------
@@ -49,7 +55,7 @@ int main(int, char**) {
     Scalar const alpha = advection_coefficient * h / d;
     Scalar const delta = diffusion_coefficient * h / (d * d);
 
-    // transport matrices (assumes dirichlet boundary conditions identically zero)
+    // transport matrices
     SparseMatrix<Scalar> const advection_matrix = alpha * d_x_first_order(dim);
     SparseMatrix<Scalar> const diffusion_matrix = delta * d_x2_first_order(dim);
     SparseMatrix<Scalar> const reaction_matrix = h * diagonal_ones(dim) * reaction_coefficients.asDiagonal();

simucene/matrix_builder.cpp

@@ -15,6 +15,12 @@ MatrixBuilder& MatrixBuilder::stripe(int32_t k, Scalar value) {
     return *this;
 }
 
+//..................................................................................................
+MatrixBuilder& MatrixBuilder::element(int32_t row, int32_t col, Scalar value) {
+    triplets_.emplace_back(row, col, value);
+    return *this;
+}
+
 //..................................................................................................
 MatrixBuilder::operator SparseMatrix<Scalar>() const {
     SparseMatrix<Scalar> result(n_, n_);

simucene/matrix_builder.h

@@ -11,8 +11,11 @@ namespace simucene {
 class MatrixBuilder {
 public:
     MatrixBuilder(int32_t n): n_(n) {}
+
     // k = 0 means on the diagonal, 1 means one above the diagonal, -1 one below, etc.
     MatrixBuilder& stripe(int32_t k, Scalar value);
+    MatrixBuilder& element(int32_t row, int32_t col, Scalar value);
+
     operator SparseMatrix<Scalar>() const;
 
 private: