1 <?xml version="1.0" encoding="UTF-8"?>
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24 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="PDE">
26 <refname>PDE</refname>
27 <refpurpose>1D PDE block</refpurpose>
30 <title>Block Screenshot</title>
34 <imagedata fileref="../../../../images/palettes/PDE.png" align="center" valign="middle"/>
39 <refsection id="Contents_PDE">
40 <title>Contents</title>
44 <link linkend="PDE">1D PDE block</link>
51 <xref linkend="Palette_PDE">Palette</xref>
56 <xref linkend="Description_PDE">Description</xref>
61 <xref linkend="Dialogbox_PDE">Dialog box</xref>
66 <xref linkend="Defaultproperties_PDE">Default properties</xref>
71 <xref linkend="Interfacingfunction_PDE">Interfacing function</xref>
78 <refsection id="Palette_PDE">
79 <title>Palette</title>
83 <link linkend="Demonstrationsblocks_pal">Demonstrations blocks palette</link>
88 <refsection id="Description_PDE">
89 <title>Description</title>
91 This block is an implementation of several numerical schemes (Finite Elements (1st and 2nd order),
92 Finite Differences (1st and 2nd order), Finite Volumes (1st order)) to solve mono-dimensional
93 PDE (Partial Differential Equation) within Xcos.
94 The mathematical framework is restricted to PDEs linear scalars with maximum order 2 in time and space.
95 The goal is to provide engineers and physicists with an easy-to-use toolbox in Xcos that will let them
96 graphically describe the PDE to be solved. A decision system selects the most efficient numerical scheme
97 depending on the type of the PDE and runs the solver.
100 <refsection id="Dialogbox_PDE">
101 <title>Dialog box</title>
105 <imagedata fileref="../../../../images/gui/PDE_gui.gif" align="center" valign="middle"/>
115 <emphasis role="bold">Domain</emphasis>
117 <para> a and b : (double) The two edges of the discretization field.</para>
121 <emphasis role="bold">PDE specification</emphasis>
125 Check boxes to select the PDE operators.
126 ai(x), bi(t) (i=1:7) are the operator coefficients.
129 Discriminant type : constant or variable, in the
130 later case, the sign should be given.
136 <emphasis role="bold">Discretization method</emphasis>
140 Choice (check box) : is the choice for the manual or the automatic mode.
143 Type : in the manual mode we can give the method type
144 (Finite differences, finite elements or finite volumes).
147 Degree : method degree (1 or 2 for the FD and FE methods,
148 1 for the FV method).
151 Number of nodes : to give the number of the nodal points.
157 <emphasis role="bold">Initial Conditions</emphasis>
159 <para> u(x,t0)=, du/dt at t0= : to give the initial conditions. </para>
163 <emphasis role="bold">Boundary condition on a</emphasis>
167 Type : two types of boundary conditions are possible : Dirichlet or Neumann.
170 Expression : to give the boundary conditions expression.
176 <emphasis role="bold">Measurement points</emphasis>
178 <para> To give the list of measurement points. </para>
182 <emphasis role="bold">Name</emphasis>
184 <para> A getvalue box to give the block's name. </para>
188 <refsection id="Defaultproperties_PDE">
189 <title>Default properties</title>
193 <emphasis role="bold">always active:</emphasis> yes
198 <emphasis role="bold">direct-feedthrough:</emphasis> no
203 <emphasis role="bold">zero-crossing:</emphasis> no
208 <emphasis role="bold">mode:</emphasis> no
213 <emphasis role="bold">regular inputs:</emphasis>
216 <emphasis role="bold">- port 1 : size [1,1] / type 1</emphasis>
219 <emphasis role="bold">- port 2 : size [1,1] / type 0</emphasis>
222 <emphasis role="bold">- port 3 : size [1,1] / type 0</emphasis>
225 <emphasis role="bold">- port 4 : size [1,1] / type 0</emphasis>
228 <emphasis role="bold">- port 5 : size [1,1] / type 1</emphasis>
233 <emphasis role="bold">regular outputs:</emphasis>
236 <emphasis role="bold">- port 1 : size [10,1] / type 1</emphasis>
239 <emphasis role="bold">- port 2 : size [0,1] / type 1</emphasis>
244 <emphasis role="bold">number/sizes of activation inputs:</emphasis> 0
249 <emphasis role="bold">number/sizes of activation outputs:</emphasis> 0
254 <emphasis role="bold">continuous-time state:</emphasis> yes
259 <emphasis role="bold">discrete-time state:</emphasis> no
264 <emphasis role="bold">object discrete-time state:</emphasis> no
269 <emphasis role="bold">name of computational function:</emphasis>
270 <emphasis role="italic">PDE</emphasis>
275 <refsection id="Interfacingfunction_PDE">
276 <title>Interfacing function</title>
279 <para> SCI/modules/scicos_blocks/macros/PDE/PDE.sci</para>
283 <refsection id="Computationalfunction_PDE">
284 <title>Computational functions</title>
287 <para> SCI/modules/scicos_blocks/macros/PDE/</para>