OptFEM2DP1 Toolbox  V1.2b3
Matlab/Octave Optimized P1-Lagrange Finite Element Method in 2D
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MassWAssemblingP1OptV1.m File Reference

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

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Functions

function M = MassWAssemblingP1OptV1 (nq, nme, me, areas, Tw)
 Assembly of the Weighted Mass Matrix using $P_1$-Lagrange finite elements.
 

Detailed Description

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

  • OptV1 version (see report).

Definition in file MassWAssemblingP1OptV1.m.

Function Documentation

function M = MassWAssemblingP1OptV1 (   nq,
  nme,
  me,
  areas,
  Tw 
)

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

  • OptV1 version (see report).

The Weighted Mass Matrix $\MasseF{w}$ is given by

\[\MasseF{w}_{i,j}=\int_\DOMH w(\q)\;\FoncBase_i(\q)\; \FoncBase_j(\q)\; d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2\]

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

Example
    Th=SquareMesh(10);
    w=@(x,y) cos(x+y);
    Tw=w(Th.q(1,:),Th.q(2,:));
    Mw=MassWAssemblingP1OptV1(Th.nq,Th.nme,Th.me,Th.areas,Tw);
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Parameters
nqtotal number of nodes of the mesh, also denoted by $\nq$,
nmetotal number of triangles, also denoted by $\nme$,
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.
TwArray containing the values of $w$ at the vertices, $1\times\nq$ array (double).
$Tw(i)=w(\q^i),$ $\forall i\in\ENS{1}{\nq}$.
Return values
MGlobal weighted mass matrix, $\nq\times\nq$ sparse matrix.

Definition at line 17 of file MassWAssemblingP1OptV1.m.