OptFEM2DP1  1.0
Matlab/Octave Optimized P1-Lagrange Finite Element Method in 2D
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StiffAssemblingP1OptV0.m File Reference

Assembly of the Stiffness Matrix using $P_1$-Lagrange finite elements. More...

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Functions

function R = StiffAssemblingP1OptV0 (nq, nme, q, me, areas)
 Assembly of the Stiffness Matrix using $P_1$-Lagrange finite elements.
 

Detailed Description

Assembly of the Stiffness Matrix using $P_1$-Lagrange finite elements.

  • OptV0 version (see report).

Definition in file StiffAssemblingP1OptV0.m.

Function Documentation

function R = StiffAssemblingP1OptV0 (   nq,
  nme,
  q,
  me,
  areas 
)

Assembly of the Stiffness Matrix using $P_1$-Lagrange finite elements.

  • OptV0 version (see report).

The Stiffness Matrix $\Stiff$ is given by

\[\Stiff_{i,j}=\int_\DOMH \DOT{\GRAD\FoncBase_i(\q)}{\GRAD\FoncBase_j(\q)}d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2\]

where $\FoncBase_i$ are $P_1$-Lagrange basis functions.

Example
    Th=SquareMesh(10);
    R=StiffAssemblingP1OptV0(Th.nq,Th.nme,Th.me,Th.q,Th.areas);

OptFEM2DP1 [V1.0e] - Copyright (C) 2013 CJS (LAGA)

This file is part of OptFEM2DP1. OptFEM2DP1 is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

OptFEM2DP1 is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

Parameters
nqtotal number of nodes of the mesh, also denoted by $\nq$.
nmetotal number of triangles, also denoted by $\nme$.
qArray of vertices coordinates, $2\times\nq$ array.
${\q}(\il,j)$ is the $\il$-th coordinate of the $j$-th vertex, $\il\in\{1,2\}$ and $j\in\ENS{1}{\nq}$
meConnectivity array, $3\times\nme$ array.
$\me(\jl,k)$ is the storage index of the $\jl$-th vertex of the $k$-th triangle in the array $\q$ of vertices coordinates, $\jl\in\{1,2,3\}$ and $k\in{\ENS{1}{\nme}}$.
areasArray of areas, $1\times\nme$ array. areas(k) is the area of the $k$-th triangle.
Return values
RStiffness Matrix, $\nq\times\nq$ sparse matrix.

Definition at line 17 of file StiffAssemblingP1OptV0.m.