540 lines
24 KiB
C
540 lines
24 KiB
C
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/********************************************************
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* ██████╗ ██████╗████████╗██╗
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* ██╔════╝ ██╔════╝╚══██╔══╝██║
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* ██║ ███╗██║ ██║ ██║
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* ██║ ██║██║ ██║ ██║
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* ╚██████╔╝╚██████╗ ██║ ███████╗
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* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
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* Geophysical Computational Tools & Library (GCTL)
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*
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* Copyright (c) 2023 Yi Zhang (yizhang-geo@zju.edu.cn)
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*
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* GCTL is distributed under a dual licensing scheme. You can redistribute
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* it and/or modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation, either version 2
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* of the License, or (at your option) any later version. You should have
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* received a copy of the GNU Lesser General Public License along with this
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* program. If not, see <http://www.gnu.org/licenses/>.
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*
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* If the terms and conditions of the LGPL v.2. would prevent you from using
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* the GCTL, please consider the option to obtain a commercial license for a
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* fee. These licenses are offered by the GCTL's original author. As a rule,
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* licenses are provided "as-is", unlimited in time for a one time fee. Please
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* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
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* to include some description of your company and the realm of its activities.
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* Also add information on how to contact you by electronic and paper mail.
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******************************************************/
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#ifndef _GCTL_SHAPEFUNC_H
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#define _GCTL_SHAPEFUNC_H
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#include "../gctl_config.h"
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#include "../core/enum.h"
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#include "../core/exceptions.h"
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#include "../maths/mathfunc.h"
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namespace gctl
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{
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enum eshape_value_e
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{
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VecValue, // Original vector components
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VecGradient, // Gradients of the vector components
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VecCurl, // Curl components
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};
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/**
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* @brief The 1st order (linear) shape functions
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*/
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class linear_sf
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{
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public:
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linear_sf(){}
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virtual ~linear_sf(){}
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/**
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* @brief Shape function defined on a 1D line.
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*
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* This function has two nodes on the left and right ends, respectively.
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* index for the left node function is 0. And the node's index is 1.
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* 0-----------1-----> x
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*
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* @param[in] x independent variable
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* @param[in] x1 low bound of the shape function
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* @param[in] x2 high bound of the shape function
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* @param[in] idx Node index
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* @param[in] vt Calculation target. Could be Value or Dx
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*
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* @return Value of the shape function
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*/
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double line(double x, double x1, double x2, size_t idx, gradient_type_e vt = Value);
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/**
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* @brief Shape function defined on a 2D rectangle.
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*
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* This function has four nodes on the corners, respectively.
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* index of the nodes are as show
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*
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* y
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* |
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* |
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* 3----------2
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* | |
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* | |
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* | |
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* | |
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* 0----------1--->x
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*
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* @param[in] x independent variable x
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* @param[in] y independent variable y
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* @param[in] x1 low bound of x
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* @param[in] x2 high bound of x
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* @param[in] y1 low bound of y
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* @param[in] y2 high bound of y
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* @param[in] idx Node index
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* @param[in] vt Calculation target. Could be Value, Dx or Dy
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*
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* @return Value of the shape function
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*/
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double quad(double x, double y, double x1, double x2, double y1, double y2,
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size_t idx, gradient_type_e vt = Value);
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/**
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* @brief Shape function defined on a 2D triangle.
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*
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* This function has three nodes on the corners, respectively.
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* index of the nodes are as show
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*
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* y
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* |
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* |
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* 2
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* | \
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* | \
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* | \
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* | \
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* | \
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* | \
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* 0-------------1--->x
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*
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* @param[in] x independent variable x
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* @param[in] y independent variable y
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* @param[in] x1 x coordinate of the first node of the triangle
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* @param[in] x2 x coordinate of the second node of the triangle
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* @param[in] x3 x coordinate of the third node of the triangle
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* @param[in] y1 y coordinate of the first node of the triangle
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* @param[in] y2 y coordinate of the second node of the triangle
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* @param[in] y3 y coordinate of the third node of the triangle
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* @param[in] idx Node index
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* @param[in] vt Calculation target. Could be Value, Dx or Dy
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*
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* @return Value of the shape function
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*/
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double triangle(double x, double y, double x1, double x2, double x3,
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double y1, double y2, double y3, size_t idx, gradient_type_e vt = Value);
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/**
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* @brief Interpolate using the triangular linear shape function
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*
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* This function has three nodes on the corners, respectively.
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* index of the nodes are as show
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*
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* y
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* |
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* |
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* 2
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* | \
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* | \
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* | \
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* | \
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* | \
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* | \
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* 0-------------1--->x
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*
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* @param[in] x independent variable x
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* @param[in] y independent variable y
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* @param[in] x1 x coordinate of the first node of the triangle
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* @param[in] x2 x coordinate of the second node of the triangle
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* @param[in] x3 x coordinate of the third node of the triangle
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* @param[in] y1 y coordinate of the first node of the triangle
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* @param[in] y2 y coordinate of the second node of the triangle
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* @param[in] y3 y coordinate of the third node of the triangle
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* @param[in] v1 value at the first node of the triangle
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* @param[in] v2 value at the second node of the triangle
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* @param[in] v3 value at of the third node of the triangle
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*
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* @return Value of the interpolation
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*/
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double triangle_interpolate(double x, double y, double x1, double x2, double x3,
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double y1, double y2, double y3, double v1, double v2, double v3, gradient_type_e vt);
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/**
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* @brief Shape function defined on a 3D cube.
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*
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* This function has eight nodes on the corners, respectively.
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* index of the nodes are as show
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* z
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* |
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* | 7----------6
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* | /| /|
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* | / | / |
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* |/ | / |
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* 4----------5 |
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* | 3 | 2
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* | /-------|--/
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* | / | /
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* 0----------1--------> x
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*
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* @param[in] x independent variable x
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* @param[in] y independent variable y
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* @param[in] z independent variable z
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* @param[in] x1 low bound of x
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* @param[in] x2 high bound of x
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* @param[in] y1 low bound of y
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* @param[in] y2 high bound of y
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* @param[in] z1 low bound of z
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* @param[in] z2 high bound of z
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* @param[in] idx Node index
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* @param[in] vt Calculation target. Could be Value, Dx, Dy or Dz
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*
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* @return Value of the shape function
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*/
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double cube(double x, double y, double z, double x1, double x2,
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double y1, double y2, double z1, double z2, size_t idx, gradient_type_e vt = Value);
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/**
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* @brief Shape function defined on a 3D tetrahedron.
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*
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* This function has four nodes on the corners, respectively.
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* index of the nodes are as show
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* zta
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* |
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* 3
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* |\
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* | \
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* | \
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* | \
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* | \
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* | \
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* 0------------2---> eta
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* | /
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* | /
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* | /
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* | /
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* | /
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* | /
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* |/
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* 1
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* |
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* ksi
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*
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* @param[in] ksi local coordinate ksi
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* @param[in] eta local coordinate eta
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* @param[in] zta local coordinate zta
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* @param[in] x1 x coordinate of the first node of the tetrahedron
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* @param[in] x2 x coordinate of the second node of the tetrahedron
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* @param[in] x3 x coordinate of the third node of the tetrahedron
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* @param[in] x4 x coordinate of the fourth node of the tetrahedron
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* @param[in] y1 y coordinate of the first node of the tetrahedron
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* @param[in] y2 y coordinate of the second node of the tetrahedron
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* @param[in] y3 y coordinate of the third node of the tetrahedron
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* @param[in] y4 y coordinate of the fourth node of the tetrahedron
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* @param[in] z1 z coordinate of the first node of the tetrahedron
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* @param[in] z2 z coordinate of the second node of the tetrahedron
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* @param[in] z3 z coordinate of the third node of the tetrahedron
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* @param[in] z4 z coordinate of the fourth node of the tetrahedron
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* @param[in] idx Node index
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* @param[in] vt Calculation target. Could be Value, Dx, Dy or Dz
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*
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* @return Value of the shape function
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*/
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double tetrahedron(double ksi, double eta, double zta, double x1, double x2, double x3, double x4,
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double y1, double y2, double y3, double y4, double z1, double z2, double z3, double z4,
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size_t idx, gradient_type_e vt = Value);
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/**
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* @brief transform local coordinates to global ones within a tetrahedron element
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*
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* @param[out] x global coordinate x
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* @param[out] y global coordinate y
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* @param[out] z global coordinate z
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* @param[in] ksi local coordinate ksi
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* @param[in] eta local coordinate eta
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* @param[in] zta local coordinate zta
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* @param[in] x1 x coordinate of the first node of the tetrahedron
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* @param[in] x2 x coordinate of the second node of the tetrahedron
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* @param[in] x3 x coordinate of the third node of the tetrahedron
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* @param[in] x4 x coordinate of the fourth node of the tetrahedron
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* @param[in] y1 y coordinate of the first node of the tetrahedron
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* @param[in] y2 y coordinate of the second node of the tetrahedron
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* @param[in] y3 y coordinate of the third node of the tetrahedron
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* @param[in] y4 y coordinate of the fourth node of the tetrahedron
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* @param[in] z1 z coordinate of the first node of the tetrahedron
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* @param[in] z2 z coordinate of the second node of the tetrahedron
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* @param[in] z3 z coordinate of the third node of the tetrahedron
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* @param[in] z4 z coordinate of the fourth node of the tetrahedron
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*/
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void local2global_tetrahedron(double &x, double &y, double &z, double ksi, double eta, double zta,
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double x1, double x2, double x3, double x4, double y1, double y2, double y3, double y4,
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double z1, double z2, double z3, double z4);
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/**
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* @brief transform global coordinates to local ones within a tetrahedron element
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*
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* @param[out] ksi local coordinate ksi
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* @param[out] eta local coordinate eta
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* @param[out] zta local coordinate zta
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* @param[in] x global coordinate x
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* @param[in] y global coordinate y
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* @param[in] z global coordinate z
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* @param[in] x1 x coordinate of the first node of the tetrahedron
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* @param[in] x2 x coordinate of the second node of the tetrahedron
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* @param[in] x3 x coordinate of the third node of the tetrahedron
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* @param[in] x4 x coordinate of the fourth node of the tetrahedron
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* @param[in] y1 y coordinate of the first node of the tetrahedron
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* @param[in] y2 y coordinate of the second node of the tetrahedron
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* @param[in] y3 y coordinate of the third node of the tetrahedron
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* @param[in] y4 y coordinate of the fourth node of the tetrahedron
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* @param[in] z1 z coordinate of the first node of the tetrahedron
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* @param[in] z2 z coordinate of the second node of the tetrahedron
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* @param[in] z3 z coordinate of the third node of the tetrahedron
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* @param[in] z4 z coordinate of the fourth node of the tetrahedron
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*/
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void global2local_tetrahedron(double &ksi, double &eta, double &zta, double x, double y, double z,
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double x1, double x2, double x3, double x4, double y1, double y2, double y3, double y4,
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double z1, double z2, double z3, double z4);
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/**
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* @brief Interpolate using the tetrahedral linear shape function
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*
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* @param[in] x global coordinate x
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* @param[in] y global coordinate y
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* @param[in] z global coordinate z
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* @param[in] x1 x coordinate of the first node of the tetrahedron
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* @param[in] x2 x coordinate of the second node of the tetrahedron
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* @param[in] x3 x coordinate of the third node of the tetrahedron
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* @param[in] x4 x coordinate of the fourth node of the tetrahedron
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* @param[in] y1 y coordinate of the first node of the tetrahedron
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* @param[in] y2 y coordinate of the second node of the tetrahedron
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* @param[in] y3 y coordinate of the third node of the tetrahedron
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* @param[in] y4 y coordinate of the fourth node of the tetrahedron
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* @param[in] z1 z coordinate of the first node of the tetrahedron
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* @param[in] z2 z coordinate of the second node of the tetrahedron
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* @param[in] z3 z coordinate of the third node of the tetrahedron
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* @param[in] z4 z coordinate of the fourth node of the tetrahedron
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* @param vt Value type
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*/
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double tetrahedron_interpolate(double x, double y, double z, double x1, double x2, double x3, double x4,
|
|||
|
|
double y1, double y2, double y3, double y4, double z1, double z2, double z3, double z4,
|
|||
|
|
double v1, double v2, double v3, double v4, gradient_type_e vt = Value);
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* @brief Shape function defined on a 3D triangular prism.
|
|||
|
|
*
|
|||
|
|
* This function has six nodes on the corners, respectively. Index of the nodes are as show.
|
|||
|
|
*
|
|||
|
|
* zta eta
|
|||
|
|
* | / 3(0,1,1)
|
|||
|
|
* | / /|\
|
|||
|
|
* |/ / | \
|
|||
|
|
* | / | \
|
|||
|
|
* | / / \0(0,1,0)
|
|||
|
|
* | 4|---------| 5
|
|||
|
|
* | | / \ |
|
|||
|
|
* | |/-------\|
|
|||
|
|
* | 1(0,0,0) 2(1,0,0)
|
|||
|
|
* O-----------------> ksi
|
|||
|
|
*
|
|||
|
|
* @param[in] ksi local coordinate ksi
|
|||
|
|
* @param[in] eta local coordinate eta
|
|||
|
|
* @param[in] zta local coordinate zta
|
|||
|
|
* @param[in] xs x coordinates of the nodes of the prism, must be in length of six
|
|||
|
|
* @param[in] ys y coordinates of the nodes of the prism, must be in length of six
|
|||
|
|
* @param[in] zs z coordinates of the nodes of the prism, must be in length of six
|
|||
|
|
* @param[in] idx node index of the calculation
|
|||
|
|
* @param[in] vt Calculation target. Could be Value, Dx, Dy or Dz
|
|||
|
|
* @return Value of the shape function
|
|||
|
|
*/
|
|||
|
|
double triprism(double ksi, double eta, double zta, double *xs, double *ys, double *zs, size_t idx, gradient_type_e vt = Value);
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* @brief transform local coordinates to global ones within a triangular prism element
|
|||
|
|
*
|
|||
|
|
* @param[out] x global coordinate x
|
|||
|
|
* @param[out] y global coordinate y
|
|||
|
|
* @param[out] z global coordinate z
|
|||
|
|
* @param[in] ksi local coordinate ksi
|
|||
|
|
* @param[in] eta local coordinate eta
|
|||
|
|
* @param[in] zta local coordinate zta
|
|||
|
|
* @param[in] xs x coordinates of the nodes of the prism, must be in length of six
|
|||
|
|
* @param[in] ys y coordinates of the nodes of the prism, must be in length of six
|
|||
|
|
* @param[in] zs z coordinates of the nodes of the prism, must be in length of six
|
|||
|
|
*/
|
|||
|
|
void local2global_triprism(double &x, double &y, double &z, double ksi, double eta, double zta,
|
|||
|
|
double *xs, double *ys, double *zs);
|
|||
|
|
};
|
|||
|
|
|
|||
|
|
class linear_esf
|
|||
|
|
{
|
|||
|
|
public:
|
|||
|
|
linear_esf(){}
|
|||
|
|
virtual ~linear_esf(){}
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* @brief Edge based vector shape function defined on a 2D triangle.
|
|||
|
|
*
|
|||
|
|
* This function has three nodes on the corners, respectively.
|
|||
|
|
* Indice of the nodes and edges are as show.
|
|||
|
|
*
|
|||
|
|
* y
|
|||
|
|
* |
|
|||
|
|
* |
|
|||
|
|
* 2
|
|||
|
|
* | \
|
|||
|
|
* | \
|
|||
|
|
* | \
|
|||
|
|
* | \
|
|||
|
|
* | \
|
|||
|
|
* | \
|
|||
|
|
* 0-------------1--->x
|
|||
|
|
* edge0: 0->1
|
|||
|
|
* edge1: 1->2
|
|||
|
|
* edge2: 2->0
|
|||
|
|
*
|
|||
|
|
* @param[in] x Evaluation position x
|
|||
|
|
* @param[in] y Evaluation position y
|
|||
|
|
* @param[in] x1 x coordinate of the first node of the triangle
|
|||
|
|
* @param[in] x2 x coordinate of the second node of the triangle
|
|||
|
|
* @param[in] x3 x coordinate of the third node of the triangle
|
|||
|
|
* @param[in] y1 y coordinate of the first node of the triangle
|
|||
|
|
* @param[in] y2 y coordinate of the second node of the triangle
|
|||
|
|
* @param[in] y3 y coordinate of the third node of the triangle
|
|||
|
|
* @param[in] idx Edge index
|
|||
|
|
* @param[in] vt Calculation target. Could be Value, Gradient or Curl
|
|||
|
|
* @param[in] ot Ordering direction of the edge's nodes
|
|||
|
|
* @param xval Evaluated shape function. Equals to Vx (Value), dVx/dy (Gradient) or curl(V) (Curl)
|
|||
|
|
* @param yval Evaluated shape function. Equals to Vy (Value), dVy/dx (Gradient) or curl(V) (Curl)
|
|||
|
|
*/
|
|||
|
|
void triangle(double x, double y, double x1, double x2, double x3,
|
|||
|
|
double y1, double y2, double y3, size_t idx, eshape_value_e vt,
|
|||
|
|
edge_orient_e ot, double &xval, double &yval);
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* @brief Edge based vector shape function defined on a 3D tetrahedron.
|
|||
|
|
*
|
|||
|
|
* This function has four nodes on the corners, respectively.
|
|||
|
|
* Indice of the nodes and edges are as show.
|
|||
|
|
*
|
|||
|
|
* q
|
|||
|
|
* |
|
|||
|
|
* 3
|
|||
|
|
* |\
|
|||
|
|
* | \
|
|||
|
|
* | \
|
|||
|
|
* | \
|
|||
|
|
* | \
|
|||
|
|
* | \
|
|||
|
|
* 0------------2---> v
|
|||
|
|
* | /
|
|||
|
|
* | /
|
|||
|
|
* | /
|
|||
|
|
* | /
|
|||
|
|
* | /
|
|||
|
|
* | /
|
|||
|
|
* |/
|
|||
|
|
* 1
|
|||
|
|
* |
|
|||
|
|
* u
|
|||
|
|
*
|
|||
|
|
* edge0: 0->1
|
|||
|
|
* edge1: 0->2
|
|||
|
|
* edge2: 0->3
|
|||
|
|
* edge3: 1->2
|
|||
|
|
* edge4: 1->3 (or 3->1 in some other implementations, Does not really matter ^,^)
|
|||
|
|
* edge5: 2->3
|
|||
|
|
*
|
|||
|
|
* @param[in] x Evaluation position x
|
|||
|
|
* @param[in] y Evaluation position y
|
|||
|
|
* @param[in] z Evaluation position z
|
|||
|
|
* @param[in] x1 x coordinate of the first node of the tetrahedron
|
|||
|
|
* @param[in] x2 x coordinate of the second node of the tetrahedron
|
|||
|
|
* @param[in] x3 x coordinate of the third node of the tetrahedron
|
|||
|
|
* @param[in] x4 x coordinate of the fourth node of the tetrahedron
|
|||
|
|
* @param[in] y1 y coordinate of the first node of the tetrahedron
|
|||
|
|
* @param[in] y2 y coordinate of the second node of the tetrahedron
|
|||
|
|
* @param[in] y3 y coordinate of the third node of the tetrahedron
|
|||
|
|
* @param[in] y4 y coordinate of the fourth node of the tetrahedron
|
|||
|
|
* @param[in] z1 z coordinate of the first node of the tetrahedron
|
|||
|
|
* @param[in] z2 z coordinate of the second node of the tetrahedron
|
|||
|
|
* @param[in] z3 z coordinate of the third node of the tetrahedron
|
|||
|
|
* @param[in] z4 z coordinate of the fourth node of the tetrahedron
|
|||
|
|
* @param[in] idx Edge index
|
|||
|
|
* @param[in] vt Calculation target. Could be Value, Curl or Div
|
|||
|
|
* @param[in] ot Ordering direction of the edge's nodes
|
|||
|
|
* @param xval Evaluated shape function. Equals to Vx (Value), dVx/dy (Gradient) or curl(V)_x (Curl)
|
|||
|
|
* @param yval Evaluated shape function. Equals to Vy (Value), dVy/dx (Gradient) or curl(V)_y (Curl)
|
|||
|
|
* @param zval Evaluated shape function. Equals to Vz (Value), dVz/dx (Gradient) or curl(V)_z (Curl)
|
|||
|
|
* @param xval2 Evaluated shape function. Equals to dVx/dz (Gradient)
|
|||
|
|
* @param yval2 Evaluated shape function. Equals to dVy/dz (Gradient)
|
|||
|
|
* @param zval2 Evaluated shape function. Equals to dVz/dy (Gradient)
|
|||
|
|
*/
|
|||
|
|
void tetrahedron(double x, double y, double z, double x1, double x2, double x3, double x4,
|
|||
|
|
double y1, double y2, double y3, double y4, double z1, double z2, double z3, double z4,
|
|||
|
|
size_t idx, eshape_value_e vt, edge_orient_e ot, double &xval, double &yval, double &zval,
|
|||
|
|
double &xval2, double &yval2, double &zval2);
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* @brief Edge based vector shape function defined on a 3D cube.
|
|||
|
|
*
|
|||
|
|
* This function has eight nodes on the corners, respectively.
|
|||
|
|
* index of the nodes and edges are as show.
|
|||
|
|
* z
|
|||
|
|
* |
|
|||
|
|
* | 7----------6
|
|||
|
|
* | /| /|
|
|||
|
|
* | / | / |
|
|||
|
|
* |/ | / |
|
|||
|
|
* 4----------5 |
|
|||
|
|
* | 3 -----|-- 2
|
|||
|
|
* | / | /
|
|||
|
|
* | / | /
|
|||
|
|
* 0----------1--------> x
|
|||
|
|
*
|
|||
|
|
* edge0: 0->1
|
|||
|
|
* edge1: 3->2
|
|||
|
|
* edge2: 4->5
|
|||
|
|
* edge3: 7->6
|
|||
|
|
* edge4: 0->3
|
|||
|
|
* edge5: 1->2
|
|||
|
|
* edge6: 4->7
|
|||
|
|
* edge7: 5->6
|
|||
|
|
* edge8: 0->4
|
|||
|
|
* edge9: 1->5
|
|||
|
|
* edge10: 3->7
|
|||
|
|
* edge11: 2->6
|
|||
|
|
*
|
|||
|
|
* @param[in] x Evaluation variable x
|
|||
|
|
* @param[in] y Evaluation variable y
|
|||
|
|
* @param[in] z Evaluation variable z
|
|||
|
|
* @param[in] x1 low bound of x
|
|||
|
|
* @param[in] x2 high bound of x
|
|||
|
|
* @param[in] y1 low bound of y
|
|||
|
|
* @param[in] y2 high bound of y
|
|||
|
|
* @param[in] z1 low bound of z
|
|||
|
|
* @param[in] z2 high bound of z
|
|||
|
|
* @param[in] idx Edge index
|
|||
|
|
* @param[in] vt Calculation target. Could be Value, Curl or Div
|
|||
|
|
* @param[in] ot Ordering direction of the edge's nodes
|
|||
|
|
* @param xval Evaluated shape function. Equals to Vx (Value), dVx/dy (Gradient) or curl(V)_x (Curl)
|
|||
|
|
* @param yval Evaluated shape function. Equals to Vy (Value), dVy/dx (Gradient) or curl(V)_y (Curl)
|
|||
|
|
* @param zval Evaluated shape function. Equals to Vz (Value), dVz/dx (Gradient) or curl(V)_z (Curl)
|
|||
|
|
* @param xval2 Evaluated shape function. Equals to dVx/dz (Gradient)
|
|||
|
|
* @param yval2 Evaluated shape function. Equals to dVy/dz (Gradient)
|
|||
|
|
* @param zval2 Evaluated shape function. Equals to dVz/dy (Gradient)
|
|||
|
|
*/
|
|||
|
|
void cube(double x, double y, double z, double x1, double x2, double y1, double y2, double z1, double z2,
|
|||
|
|
size_t idx, eshape_value_e vt, edge_orient_e ot, double &xval, double &yval, double &zval,
|
|||
|
|
double &xval2, double &yval2, double &zval2);
|
|||
|
|
};
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
#endif // _GCTL_SHAPEFUNC_H
|