From: David Wells Date: Tue, 5 May 2020 16:10:32 +0000 (-0400) Subject: Remove some non-ascii characters. X-Git-Tag: v9.2.0-rc1~125^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F10038%2Fhead;p=dealii.git Remove some non-ascii characters. My copy of pdflatex does not like (i.e., I cannot compile the doxygen-generated file _formulas.tex) math statements with unicode MINUS SIGN instead of the old ASCII HYPHEN-MINUS. While here I also switched out RIGHT SINGLE QUOTATION MARK for (also ASCII) APOSTROPHE and made a few other small changes. We should be, in general, able to use unicode in our documentation outside of math mode so I didn't change those usages unless they seemed gramatically incorrect to me (like using the right quotation mark instead of an apostrophe). --- diff --git a/include/deal.II/base/tensor_product_polynomials.h b/include/deal.II/base/tensor_product_polynomials.h index 9b36fabe87..c6bec0062d 100644 --- a/include/deal.II/base/tensor_product_polynomials.h +++ b/include/deal.II/base/tensor_product_polynomials.h @@ -409,7 +409,7 @@ private: const std::vector>> polynomials; /** - * Each tensor product polynomial @þ{i} is a product of one-dimensional + * Each tensor product polynomial $p_i$ is a product of one-dimensional * polynomials in each space direction. Compute the indices of these one- * dimensional polynomials for each space direction, given the index * i. diff --git a/include/deal.II/lac/utilities.h b/include/deal.II/lac/utilities.h index 2a2cfa42cb..c0211284cd 100644 --- a/include/deal.II/lac/utilities.h +++ b/include/deal.II/lac/utilities.h @@ -445,11 +445,11 @@ namespace Utilities // algorithm verbatim: // // [Y]=chebyshev_filter_scaled(X, m, a, b, aL). - // e=(b−a)/2; c=(a+b)/2; σ=e/(c−aL); τ=2/σ; - // Y=(H∗X−c∗X)∗(σ/e); + // e=(b-a)/2; c=(a+b)/2; σ=e/(c-aL); τ=2/σ; + // Y=(H∗X-c∗X)∗(σ/e); // for i=2 to m do - // σnew =1/(τ −σ); - // Yt =(H∗Y−c∗Y)∗(2∗σnew/e)−(σ∗σnew)∗X; + // σnew =1/(τ - σ); + // Yt =(H∗Y - c∗Y)∗(2∗σnew/e)-(σ∗σnew)∗X; // X =Y; Y =Yt; σ =σnew; const double e = (b - a) / 2.; diff --git a/include/deal.II/numerics/vector_tools_boundary.h b/include/deal.II/numerics/vector_tools_boundary.h index 684310cd7c..09c232a038 100644 --- a/include/deal.II/numerics/vector_tools_boundary.h +++ b/include/deal.II/numerics/vector_tools_boundary.h @@ -609,7 +609,7 @@ namespace VectorTools * L2-projection method used has been taken from the paper "Electromagnetic * scattering simulation using an H (curl) conforming hp finite element * method in three dimensions" by PD Ledger, K Morgan and O Hassan ( Int. J. - * Num. Meth. Fluids, Volume 53, Issue 8, pages 1267–1296). + * Num. Meth. Fluids, Volume 53, Issue 8, pages 1267-1296). * * This function will compute constraints that correspond to Dirichlet * boundary conditions of the form diff --git a/include/deal.II/numerics/vector_tools_boundary.templates.h b/include/deal.II/numerics/vector_tools_boundary.templates.h index 37c58a9534..a5e9d85cdc 100644 --- a/include/deal.II/numerics/vector_tools_boundary.templates.h +++ b/include/deal.II/numerics/vector_tools_boundary.templates.h @@ -2887,7 +2887,7 @@ namespace VectorTools // Electromagnetic scattering simulation using an H (curl) conforming hp // finite element method in three dimensions, PD Ledger, K Morgan, O // Hassan, Int. J. Num. Meth. Fluids, Volume 53, Issue 8, pages - // 1267–1296, 20 March 2007: + // 1267-1296, 20 March 2007: // http://onlinelibrary.wiley.com/doi/10.1002/fld.1223/abstract // Create hp FEcollection, dof_handler can be either hp or standard type. diff --git a/include/deal.II/opencascade/utilities.h b/include/deal.II/opencascade/utilities.h index 0a27831b8b..e69e5507c2 100644 --- a/include/deal.II/opencascade/utilities.h +++ b/include/deal.II/opencascade/utilities.h @@ -77,7 +77,7 @@ DEAL_II_NAMESPACE_OPEN * This is done by inheriting abstract topology classes from the TopoDS * package by those implementing a boundary representation model (from the * BRep package). Only 3 types of topological objects have geometric - * representations – vertex, edge, and face. + * representations - vertex, edge, and face. * * Every TopoDS_Shape can be queried to figure out what type of shape it is, * and actual geometrical objects, like surfaces, curves or points, can be diff --git a/include/deal.II/sundials/arkode.h b/include/deal.II/sundials/arkode.h index 6d5971f779..69fde97c39 100644 --- a/include/deal.II/sundials/arkode.h +++ b/include/deal.II/sundials/arkode.h @@ -138,19 +138,19 @@ namespace SUNDIALS * * For both DIRK and ARK methods, an implicit system of the form * \f[ - * G(z_i) \dealcoloneq M z_i − h_n A^I_{i,i} f_I (t^I_{n,i}, z_i) − a_i = 0 + * G(z_i) \dealcoloneq M z_i - h_n A^I_{i,i} f_I (t^I_{n,i}, z_i) - a_i = 0 * \f] * must be solved for each stage $z_i , i = 1, \ldots, s$, where * we have the data * \f[ * a_i \dealcoloneq - * M y_{n−1} + h_n \sum_{j=1}^{i−1} [ A^E_{i,j} f_E(t^E_{n,j}, z_j) + * M y_{n-1} + h_n \sum_{j=1}^{i-1} [ A^E_{i,j} f_E(t^E_{n,j}, z_j) * + A^I_{i,j} f_I (t^I_{n,j}, z_j)] * \f] * for the ARK methods, or * \f[ * a_i \dealcoloneq - * M y_{n−1} + h_n \sum_{j=1}^{i−1} A^I_{i,j} f_I (t^I_{n,j}, z_j) + * M y_{n-1} + h_n \sum_{j=1}^{i-1} A^I_{i,j} f_I (t^I_{n,j}, z_j) * \f] * for the DIRK methods. Here $A^I_{i,j}$ and $A^E_{i,j}$ are the Butcher's * tables for the chosen solver. @@ -162,7 +162,7 @@ namespace SUNDIALS * faster solution process. * * For systems of either type, ARKode allows a choice of solution strategy. - * The default solver choice is a variant of Newton’s method, + * The default solver choice is a variant of Newton's method, * \f[ * z_i^{m+1} = z_i^m +\delta^{m+1}, * \f] @@ -178,13 +178,13 @@ namespace SUNDIALS * \qquad \gamma\dealcoloneq h_n A^I_{i,i}. * \f] * - * As an alternate to Newton’s method, ARKode may solve for each stage $z_i ,i + * As an alternate to Newton's method, ARKode may solve for each stage $z_i ,i * = 1, \ldots , s$ using an Anderson-accelerated fixed point iteration * \f[ * z_i^{m+1} = g(z_i^{m}), m=0,1,\ldots. * \f] * - * Unlike with Newton’s method, this option does not require the solution of + * Unlike with Newton's method, this option does not require the solution of * a linear system at each iteration, instead opting for solution of a * low-dimensional least-squares solution to construct the nonlinear update. * @@ -217,7 +217,7 @@ namespace SUNDIALS * the efficiency and robustness of the algorithm intimately depends on the * choice of a good initial guess. In ARKode, the initial guess for either * nonlinear solution method is a predicted value $z_i(0)$ that is computed - * explicitly from the previously-computed data (e.g. $y_{n−2}, y_{n−1}$, and + * explicitly from the previously-computed data (e.g. $y_{n-2}, y_{n-1}$, and * $z_j$ where $j < i$). Additional information on the specific predictor * algorithms implemented in ARKode is provided in ARKode documentation. * @@ -594,7 +594,7 @@ namespace SUNDIALS * * Make sure that after a call to this function, we know how to compute * solutions of systems $A x = b$, where $A$ is some approximation to the - * Newton matrix, $M − \gamma \partial f_I/\partial y$. This function is + * Newton matrix, $M - \gamma \partial f_I/\partial y$. This function is * optional. If the user does not provide it, then solve_jacobian_system() * is assumed to also perform the setup internally. * @@ -634,7 +634,7 @@ namespace SUNDIALS * @param[in] fpred is the value of the implicit right-hand side at ypred, * $f_I (t_n, ypred)$. * - * @param[in] convfail – an input flag used to indicate any problem that + * @param[in] convfail Input flag used to indicate any problem that * occurred during the solution of the nonlinear equation on the current * time step for which the linear solver is being used. This flag can be * used to help decide whether the Jacobian data kept by a linear solver diff --git a/include/deal.II/sundials/kinsol.h b/include/deal.II/sundials/kinsol.h index 9a637da28c..3f2444ca7a 100644 --- a/include/deal.II/sundials/kinsol.h +++ b/include/deal.II/sundials/kinsol.h @@ -55,7 +55,7 @@ namespace SUNDIALS * accelerated with Anderson acceleration. KINSOL is based on the previous * Fortran package NKSOL of Brown and Saad. * - * KINSOL’s Newton solver employs the inexact Newton method. As this solver + * KINSOL's Newton solver employs the inexact Newton method. As this solver * is intended mainly for large systems, the user is required to provide * their own solver function. If a solver function is not provided, the * internal dense solver of KINSOL is used. Be warned that this solver @@ -66,7 +66,7 @@ namespace SUNDIALS * scheme: * - set $u_0$ = an initial guess * - For $n = 0, 1, 2, \ldots$ until convergence do: - * - Solve $J(u_n)\delta_n = −F(u_n)$ + * - Solve $J(u_n)\delta_n = -F(u_n)$ * - Set $u_{n+1} = u_n + \lambda \delta_n, 0 < \lambda \leq 1$ * - Test for convergence * @@ -154,14 +154,14 @@ namespace SUNDIALS * convergence is made before the iteration continues. * * For Picard iteration, as implemented in KINSOL, we consider a special form - * of the nonlinear function $F$, such that $F(u) = Lu − N(u)$, where $L$ is + * of the nonlinear function $F$, such that $F(u) = Lu - N(u)$, where $L$ is * a constant nonsingular matrix and $N$ is (in general) nonlinear. * - * Then the fixed-point function $G$ is defined as $G(u) = u − L^{-1}F(u)$. + * Then the fixed-point function $G$ is defined as $G(u) = u - L^{-1}F(u)$. * Within each iteration, the Picard step is computed then added to $u_n$ to * produce the new iterate. Next, the nonlinear residual function is * evaluated at the new iterate, and convergence is checked. The Picard and - * fixed point methods can be significantly accelerated using Anderson’s + * fixed point methods can be significantly accelerated using Anderson's * method. * * The user has to provide the implementation of the following std::functions: