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fd2d_heat_steady.html
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<html>
<head>
<title>
FD2D_HEAT_STEADY - 2D Steady State Heat Equation in a Rectangle
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FD2D_HEAT_STEADY <br> 2D Steady State Heat Equation in a Rectangle
</h1>
<hr>
<p>
<b>FD2D_HEAT_STEADY</b>
is a C++ program which
solves the steady state (time independent) heat equation in a 2D
rectangular region.
</p>
<p>
The physical region, and the boundary conditions, are suggested
by this diagram:
<pre>
U = 0, Y = 1.0
+------------------+
| |
U = 10 | | U = 100
X = 0.0 | | X = 2.0
+------------------+
U = 0, Y = 0.0
</pre>
</p>
<p>
The region is covered with a grid of NX by NY nodes, and an NX by NY
array U is used to record the temperature. The correspondence between
array indices and locations in the region is suggested by giving the
indices of the four corners:
<pre>
I = NY
+------------------+
| |
J = 1 | | J = NX
| |
+------------------+
I = 1
</pre>
</p>
<p>
The form of the steady heat equation is
<pre>
- d/dx K(x,y) du/dx - d/dy K(x,y) du/dy = F(x,y)
</pre>
where K(x,y) is the heat conductivity, and F(x,y) is a
heat source term.
</p>
<p>
By using a simple finite difference approximation, this single equation
can be replaced by NX * NY linear equations in NX * NY variables;
each equation is associated with one of the nodes in the mesh. Nodes
long the boundary generate boundary condition equations, while interior
nodes generate equations that approximate the steady heat equation.
</p>
<p>
The linear system is sparse, and can easily be solved directly in MATLAB.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>FD2D_HEAT_STEADY</b> is available in
<a href = "../../c_src/fd2d_heat_steady/fd2d_heat_steady.html">a C version</a> and
<a href = "../../cpp_src/fd2d_heat_steady/fd2d_heat_steady.html">a C++ version</a> and
<a href = "../../f77_src/fd2d_heat_steady/fd2d_heat_steady.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fd2d_heat_steady/fd2d_heat_steady.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fd2d_heat_steady/fd2d_heat_steady.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/fd1d_heat_steady/fd1d_heat_steady.html">
FD1D_HEAT_STEADY</a>,
a C++ program which
uses the finite difference method to solve the 1D Time Independent
Heat Equations.
</p>
<p>
<a href = "../../cpp_src/fem1d_heat_steady/fem1d_heat_steady.html">
FEM1D_HEAT_STEADY</a>,
a C++ program which
uses the finite element method to solve the 1D Time Independent
Heat Equations.
</p>
<p>
<a href = "../../cpp_src/fem2d_heat/fem2d_heat.html">
FEM2D_HEAT</a>,
a C++ program which
solves the 2D time dependent heat equation on the unit square.
</p>
<p>
<a href = "../../cpp_src/heated_plate/heated_plate.html">
HEATED_PLATE</a>,
a C++ program which
solves the steady state heat equation in a 2D
rectangular region, and is intended as
a starting point for a parallel version.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fd2d_heat_steady.cpp">fd2d_heat_steady.cpp</a>, the source code.
</li>
<li>
<a href = "fd2d_heat_steady.hpp">fd2d_heat_steady.hpp</a>, the include file.
</li>
<li>
<a href = "fd2d_heat_steady.sh">fd2d_heat_steady.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fd2d_heat_steady_prb.cpp">fd2d_heat_steady_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "fd2d_heat_steady_prb.sh">fd2d_heat_steady_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "fd2d_heat_steady_prb_output.txt">fd2d_heat_steady_prb_output.txt</a>,
the output file.
</li>
<li>
<a href = "test01_data.txt">test01_data.txt</a>
data defining the solution.
</li>
<li>
<a href = "test01_commands.txt">test01_commands.txt</a>
GNUPLOT commands to make an image of the solution.
</li>
<li>
<a href = "test01.png">test01.png</a>
an image of the solution.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>FD2D_HEAT_STEADY</b> solves the steady 2D heat equation.
</li>
<li>
<b>INTERIOR</b> sets up the matrix and right hand side at interior nodes.
</li>
<li>
<b>R8MAT_FS</b> factors and solves a system with one right hand side.
</li>
<li>
<b>R8VEC_LINSPACE</b> creates a vector of linearly spaced values.
</li>
<li>
<b>R8VEC_MESH_2D</b> creates a 2D mesh from X and Y vectors.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 29 August 2013.
</i>
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