From: Wolfgang Bangerth Date: Fri, 24 Feb 2023 01:43:34 +0000 (-0700) Subject: Link to the glossary entry for 'stiffness matrix'. X-Git-Tag: v9.5.0-rc1~527^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=2743abf6e199d3abc8d9b8410ab3a87f1d68d5a0;p=dealii.git Link to the glossary entry for 'stiffness matrix'. --- diff --git a/examples/doxygen/step_3_mixed.cc b/examples/doxygen/step_3_mixed.cc index 2c6ee38356..fa5e5590a6 100644 --- a/examples/doxygen/step_3_mixed.cc +++ b/examples/doxygen/step_3_mixed.cc @@ -278,7 +278,7 @@ void Step3::setup_system() // cell - a reference to the right FEValues object (constructed // with the correct mapping object, finite element, and quadrature rule), // which can be used as usual to compute the cell integrals. -// - The cell-local stiffness matrix and the right-hand-side vector have +// - The cell-local @ref GlossStiffnessMatrix "stiffness matrix" and the right-hand-side vector have // different sizes depending on the cell type (6 DoFs vs. 9 DoFs) so that // they might need to be resized for each cell. // diff --git a/examples/step-22/doc/results.dox b/examples/step-22/doc/results.dox index 5fcd81f425..d9f1a109e6 100644 --- a/examples/step-22/doc/results.dox +++ b/examples/step-22/doc/results.dox @@ -224,7 +224,7 @@ As explained during the generation of the sparsity pattern, it is important to have the numbering of degrees of freedom in mind when using preconditioners like incomplete LU decompositions. This is most conveniently visualized using the distribution of nonzero elements in -the stiffness matrix. +the @ref GlossStiffnessMatrix "stiffness matrix". If we don't do anything special to renumber degrees of freedom (i.e., without using DoFRenumbering::Cuthill_McKee, but with using diff --git a/examples/step-26/doc/intro.dox b/examples/step-26/doc/intro.dox index 1a44f628f4..0fbd2b74d4 100644 --- a/examples/step-26/doc/intro.dox +++ b/examples/step-26/doc/intro.dox @@ -75,7 +75,7 @@ $k_n$: \theta F^n \right], @f} -where $M$ is the @ref GlossMassMatrix "mass matrix" and $A$ is the stiffness matrix that results from +where $M$ is the @ref GlossMassMatrix "mass matrix" and $A$ is the @ref GlossStiffnessMatrix "stiffness matrix" that results from discretizing the Laplacian. Bringing all known quantities to the right hand side yields the linear system we have to solve in every step: @f{align*} diff --git a/examples/step-31/doc/intro.dox b/examples/step-31/doc/intro.dox index 00b0074492..3b4c95cde8 100644 --- a/examples/step-31/doc/intro.dox +++ b/examples/step-31/doc/intro.dox @@ -830,7 +830,7 @@ scheme and the current and previous time step. This being the sum of a symmetric positive definite and a symmetric positive semidefinite matrix, the result is also symmetric positive definite. Furthermore, $\frac\beta\alpha$ is a number proportional to the time step, and so becomes small whenever the mesh -is fine, damping the effect of the then ill-conditioned stiffness matrix. +is fine, damping the effect of the then ill-conditioned @ref GlossStiffnessMatrix "stiffness matrix". As a consequence, inverting this matrix with the Conjugate Gradient algorithm, using a simple preconditioner, is trivial and very cheap compared to inverting diff --git a/examples/step-31/step-31.cc b/examples/step-31/step-31.cc index f2b6017c48..4e97eff4d6 100644 --- a/examples/step-31/step-31.cc +++ b/examples/step-31/step-31.cc @@ -959,7 +959,7 @@ namespace Step31 } // The creation of the temperature matrix (or, rather, matrices, since we - // provide a temperature mass matrix and a temperature stiffness matrix, + // provide a temperature mass matrix and a temperature @ref GlossStiffnessMatrix "stiffness matrix", // that will be added together for time discretization) follows the // generation of the Stokes matrix – except that it is much easier // here since we do not need to take care of any blocks or coupling diff --git a/examples/step-32/step-32.cc b/examples/step-32/step-32.cc index 77501b5b7c..b12d84da11 100644 --- a/examples/step-32/step-32.cc +++ b/examples/step-32/step-32.cc @@ -2457,7 +2457,7 @@ namespace Step32 // having inhomogeneous boundary conditions, by just making a right hand // side at this point (compare the comments for the project() // function above): We create some matrix columns with exactly the values - // that would be entered for the temperature stiffness matrix, in case we + // that would be entered for the temperature @ref GlossStiffnessMatrix "stiffness matrix", in case we // have inhomogeneously constrained dofs. That will account for the correct // balance of the right hand side vector with the matrix system of // temperature. diff --git a/examples/step-36/doc/intro.dox b/examples/step-36/doc/intro.dox index 6e70d249e6..085bf3d7e9 100644 --- a/examples/step-36/doc/intro.dox +++ b/examples/step-36/doc/intro.dox @@ -83,7 +83,7 @@ continuous eigenvalue problem: @f[ \sum_j [(\nabla\phi_i, \varepsilon_h \sum_j (\phi_i, \phi_j) \tilde{\psi}_j\quad. @f] In matrix and vector notation, this equation then reads: @f[ A \tilde{\Psi} = \varepsilon_h M \tilde{\Psi} \quad, @f] where $A$ is -the stiffness matrix arising from the differential operator $L$, and +the @ref GlossStiffnessMatrix "stiffness matrix" arising from the differential operator $L$, and $M$ is the @ref GlossMassMatrix "mass matrix". The solution to the eigenvalue problem is an eigenspectrum $\varepsilon_{h,\ell}$, with associated eigenfunctions $\Psi_\ell=\sum_j \phi_j\tilde{\psi}_j$. diff --git a/examples/step-36/step-36.cc b/examples/step-36/step-36.cc index fc5e4bbba9..4296902ecb 100644 --- a/examples/step-36/step-36.cc +++ b/examples/step-36/step-36.cc @@ -86,7 +86,7 @@ namespace Step36 DoFHandler dof_handler; // With these exceptions: For our eigenvalue problem, we need both a - // stiffness matrix for the left hand side as well as a @ref GlossMassMatrix "mass matrix" for + // @ref GlossStiffnessMatrix "stiffness matrix" for the left hand side as well as a @ref GlossMassMatrix "mass matrix" for // the right hand side. We also need not just one solution function, but a // whole set of these for the eigenfunctions we want to compute, along // with the corresponding eigenvalues: diff --git a/examples/step-44/step-44.cc b/examples/step-44/step-44.cc index ed1e960190..72277e9050 100644 --- a/examples/step-44/step-44.cc +++ b/examples/step-44/step-44.cc @@ -2032,7 +2032,7 @@ namespace Step44 } } - // Now we build the local cell stiffness matrix and RHS vector. Since the + // Now we build the local cell @ref GlossStiffnessMatrix "stiffness matrix" and RHS vector. Since the // global and local system matrices are symmetric, we can exploit this // property by building only the lower half of the local matrix and copying // the values to the upper half. So we only assemble half of the diff --git a/examples/step-60/doc/intro.dox b/examples/step-60/doc/intro.dox index 23d3666bbe..30c7437695 100644 --- a/examples/step-60/doc/intro.dox +++ b/examples/step-60/doc/intro.dox @@ -215,7 +215,7 @@ F_{i} &\dealcoloneq& (f, v_i)_\Omega \qquad i=1,\dots,n \\ G_{\alpha} &\dealcoloneq& (g, q_\alpha)_\Gamma \qquad \alpha = 1,\dots, m. @f} -While the matrix $K$ is the standard stiffness matrix for the Poisson problem on +While the matrix $K$ is the standard @ref GlossStiffnessMatrix "stiffness matrix" for the Poisson problem on $\Omega$, and the vector $G$ is a standard right-hand-side vector for a finite element problem with forcing term $g$ on $\Gamma$, (see, for example, step-3), the matrix $C$ or its transpose $C^T$ are non-standard since they couple diff --git a/examples/step-8/doc/intro.dox b/examples/step-8/doc/intro.dox index e714ac5624..e454fc4ef5 100644 --- a/examples/step-8/doc/intro.dox +++ b/examples/step-8/doc/intro.dox @@ -280,7 +280,7 @@ We note that here and in the following, the indices $k,l$ run over spatial directions, i.e. $0\le k,l < d$, and that indices $i,j$ run over degrees of freedom. -The local stiffness matrix on cell $K$ therefore has the following entries: +The local @ref GlossStiffnessMatrix "stiffness matrix" on cell $K$ therefore has the following entries: @f[ A^K_{ij} = diff --git a/examples/step-8/step-8.cc b/examples/step-8/step-8.cc index c5b4c3cbfb..248f3c8d49 100644 --- a/examples/step-8/step-8.cc +++ b/examples/step-8/step-8.cc @@ -308,7 +308,7 @@ namespace Step8 mu.value_list(fe_values.get_quadrature_points(), mu_values); right_hand_side(fe_values.get_quadrature_points(), rhs_values); - // Then assemble the entries of the local stiffness matrix and right + // Then assemble the entries of the local @ref GlossStiffnessMatrix "stiffness matrix" and right // hand side vector. This follows almost one-to-one the pattern // described in the introduction of this example. One of the few // comments in place is that we can compute the number diff --git a/examples/step-85/doc/intro.dox b/examples/step-85/doc/intro.dox index 7a0ac7767e..cc8d17a5ae 100644 --- a/examples/step-85/doc/intro.dox +++ b/examples/step-85/doc/intro.dox @@ -115,7 +115,7 @@ Depending on how $\Omega$ is located relative to $\mathcal{T}_h$, a cut between a cell, $T \in \mathcal{T}_h$, and $\Omega$ can become arbitrarily small: $|\Omega \cap T | \rightarrow 0$. For Neumann boundary conditions, -the consequence is that the stiffness matrix can become arbitrarily ill-conditioned +the consequence is that the @ref GlossStiffnessMatrix "stiffness matrix" can become arbitrarily ill-conditioned as the cut-size approaches zero. For a Dirichlet condition, the situation is even worse. For any finite choice of Nitsche constant, $\gamma_D$, diff --git a/include/deal.II/base/polynomial.h b/include/deal.II/base/polynomial.h index ad8d140e18..397a7d2c54 100644 --- a/include/deal.II/base/polynomial.h +++ b/include/deal.II/base/polynomial.h @@ -507,7 +507,7 @@ namespace Polynomials * * The degrees of freedom are the values at the vertices and the derivatives * at the midpoint. Currently, we do not scale the polynomials in any way, - * although better conditioning of the element stiffness matrix could + * although better conditioning of the element @ref GlossStiffnessMatrix "stiffness matrix" could * possibly be achieved with scaling. * * Calling the constructor with a given index p will generate the diff --git a/include/deal.II/fe/fe_q_bubbles.h b/include/deal.II/fe/fe_q_bubbles.h index 7f7b7046aa..0613502b65 100644 --- a/include/deal.II/fe/fe_q_bubbles.h +++ b/include/deal.II/fe/fe_q_bubbles.h @@ -54,7 +54,7 @@ DEAL_II_NAMESPACE_OPEN * the documentation of the FiniteElement class, or the one of Triangulation. * * Due to the fact that the enrichments are small almost everywhere for large - * $p$, the condition number for the mass and stiffness matrix quickly + * $p$, the condition number for the mass and @ref GlossStiffnessMatrix "stiffness matrix" quickly * increaseses with increasing $p$. Below you see a comparison with * FE_Q(QGaussLobatto(p+1)) for dim=1. * diff --git a/include/deal.II/fe/fe_values.h b/include/deal.II/fe/fe_values.h index 683a802a80..8b5e7affff 100644 --- a/include/deal.II/fe/fe_values.h +++ b/include/deal.II/fe/fe_values.h @@ -3345,7 +3345,7 @@ public: * defined by the finite element passed to `fe_values`, and `j` taking * on a specified subset of `i`'s range, starting at `i` itself and ending at * the number of cell degrees of freedom. In this way, we can construct the - * upper half and the diagonal of a stiffness matrix contribution (assuming it + * upper half and the diagonal of a @ref GlossStiffnessMatrix "stiffness matrix" contribution (assuming it * is symmetric, and that only one half of it needs to be computed), for * example. * @@ -3379,7 +3379,7 @@ public: * defined by the finite element passed to `fe_values`, and `j` taking * on a specified subset of `i`'s range, starting at zero and ending at * `i` itself. In this way, we can construct the lower half and the - * diagonal of a stiffness matrix contribution (assuming it is symmetric, and + * diagonal of a @ref GlossStiffnessMatrix "stiffness matrix" contribution (assuming it is symmetric, and * that only one half of it needs to be computed), for example. * * @note If the @p end_dof_index is equal to zero, then the returned index diff --git a/include/deal.II/lac/affine_constraints.h b/include/deal.II/lac/affine_constraints.h index 816a61f6f2..4e23d2bcb6 100644 --- a/include/deal.II/lac/affine_constraints.h +++ b/include/deal.II/lac/affine_constraints.h @@ -1231,7 +1231,7 @@ public: * situation could be where one wants to assemble of a right hand side * vector on a problem with inhomogeneous constraints, but the global matrix * has been assembled previously. A typical example of this is a time - * stepping algorithm where the stiffness matrix is assembled once, and the + * stepping algorithm where the @ref GlossStiffnessMatrix "stiffness matrix" is assembled once, and the * right hand side updated every time step. Note that, however, the entries * in the columns of the local matrix have to be exactly the same as those * that have been written into the global matrix. Otherwise, this function diff --git a/include/deal.II/lac/tensor_product_matrix.h b/include/deal.II/lac/tensor_product_matrix.h index fdf96c24d9..05bb5f6dd8 100644 --- a/include/deal.II/lac/tensor_product_matrix.h +++ b/include/deal.II/lac/tensor_product_matrix.h @@ -343,7 +343,7 @@ namespace internal * A class similar to TensorProductMatrixSymmetricSum. * * The class TensorProductMatrixSymmetricSum stores a - * 1d @ref GlossMassMatrix "mass matrix", 1d stiffness matrix, eigenvalues and eigenvectors + * 1d @ref GlossMassMatrix "mass matrix", 1d @ref GlossStiffnessMatrix "stiffness matrix", eigenvalues and eigenvectors * for each direction. If one uses one TensorProductMatrixSymmetricSum * instance for, e.g., each cell, these quantities are stored * for each cell. There is no possibility to reuse quantities between diff --git a/include/deal.II/matrix_free/fe_evaluation.h b/include/deal.II/matrix_free/fe_evaluation.h index d074724ac5..bef5801163 100644 --- a/include/deal.II/matrix_free/fe_evaluation.h +++ b/include/deal.II/matrix_free/fe_evaluation.h @@ -1847,7 +1847,7 @@ protected: * * This observation also translates to the case when different differential * operators are implemented in a program, for example the action of a mass - * matrix for one phase of the algorithm and the action of a stiffness matrix + * matrix for one phase of the algorithm and the action of a @ref GlossStiffnessMatrix "stiffness matrix" * in another one. Only a single MatrixFree object is necessary, maintaining * full efficiency by using different local functions with the respective * implementation in separate FEEvaluation objects. In other words, a user diff --git a/include/deal.II/meshworker/local_results.h b/include/deal.II/meshworker/local_results.h index ead036e56b..f23e7f3f61 100644 --- a/include/deal.II/meshworker/local_results.h +++ b/include/deal.II/meshworker/local_results.h @@ -188,7 +188,7 @@ namespace MeshWorker * object is the result of an operation is determined by the Assembler using * them. It is also the assembler that determines how many of each * kind of object are produced (for example, an assembler may create - * both the local contributions to a mass and a stiffness matrix), and for + * both the local contributions to a mass and a @ref GlossStiffnessMatrix "stiffness matrix"), and for * setting the arrays of local results to the sizes needed. * * The interface of this class allows accessing all of this information