From 9094509c7dd54b439560e6582193f19990455c6a Mon Sep 17 00:00:00 2001
From: tokies <tobias.kies@fu-berlin.de>
Date: Mon, 12 Dec 2016 21:27:26 +0100
Subject: [PATCH] * cleaned code up a little * added documentation (partially)
* added support for interpolation in 2D
---
pdeutils/fespaces/lagrangeBasis.m | 60 +++++++++++++++++++++----------
1 file changed, 42 insertions(+), 18 deletions(-)
diff --git a/pdeutils/fespaces/lagrangeBasis.m b/pdeutils/fespaces/lagrangeBasis.m
index 53c828d..cbc5825 100644
--- a/pdeutils/fespaces/lagrangeBasis.m
+++ b/pdeutils/fespaces/lagrangeBasis.m
@@ -1,6 +1,17 @@
function B = lagrangeBasis(dim, order)
+%lagrangeBasis Initializes a lagrange basis.
+%
+% Input:
+% dim Dimension of the domain over which the basis is defined.
+% order Polynomial order of the basis.
+%
+% Return:
+% B A structure representing the basis.
+%
+% Todo:
+% Explain the basis struct.
- if ((order==1) & (dim==1))
+ if ((order==1) && (dim==1))
B = struct( ...
'dim', 1, ...
'evaluate', @D1P1Evaluate, ...
@@ -10,7 +21,7 @@ function B = lagrangeBasis(dim, order)
'order', @(grid, elementIndex)(1),...
'index', @P1Index,...
'size', @(grid)(size(grid.nodes,2)));
- elseif ((order==1) & (dim==2))
+ elseif ((order==1) && (dim==2))
B = struct( ...
'dim', 2, ...
'evaluate', @D2P1Evaluate, ...
@@ -29,15 +40,28 @@ end
-function u = P1LocalInterpolation(grid, elementIndex, f, df, ddf, dddf)
- element = grid.nodes(grid.elements(:,elementIndex));
- n = size(element,2);
- u = zeros(1,n);
- for i=1:n
- u(i) = f(element(:,i));
+function u = P1LocalInterpolation(grid, elementIndex, f, varargin)
+% IMPORTANT: f is expected to be given in global coordinates
+% Todo: docme
+
+ % Get the dimension that we are currently working in.
+ dim = size(grid.nodes,1);
+ n = dim+1;
+
+ % Retrieve the corners of the associated element.
+ % There are n=dim+1 corners per element.
+ cornerIds = grid.elements(1:n, elementIndex);
+ corners = grid.nodes(:,cornerIds);
+
+ % Evaluate f in all those corners and return the resulting vector.
+ u = zeros(n,1);
+ for i = 1:n
+ u(i) = f(corners(:,i));
end
+
end
+
function globalIndices = P1Index(grid, elementIndex, localIndices)
% Compute global indices of basis functions with given localIndices in element.
dim = size(grid.nodes,1);
@@ -49,9 +73,9 @@ end
function y = D1P1Evaluate(grid, elementIndex, localIndex, x)
switch localIndex
- case 1,
+ case 1
y = x;
- case 2,
+ case 2
y = 1-x;
end
end
@@ -59,9 +83,9 @@ end
function Dx = D1P1EvaluateJacobian(grid, elementIndex, localIndex, x)
Dx = x*0;
switch localIndex
- case 1,
+ case 1
Dx(1,:) = 1;
- case 2 ,
+ case 2
Dx(1,:) = -1;
end
end
@@ -69,11 +93,11 @@ end
function y = D2P1Evaluate(grid, elementIndex, localIndex, x)
switch localIndex
- case 1,
+ case 1
y = 1 - x(1,:) - x(2,:);
- case 2 ,
+ case 2
y = x(1,:);
- case 3,
+ case 3
y = x(2,:);
end
end
@@ -81,13 +105,13 @@ end
function Dx = D2P1EvaluateJacobian(grid, elementIndex, localIndex, x)
Dx = x*0;
switch localIndex
- case 1,
+ case 1
Dx(1,:) = -1;
Dx(2,:) = -1;
- case 2 ,
+ case 2
Dx(1,:) = 1;
Dx(2,:) = 0;
- case 3,
+ case 3
Dx(1,:) = 0;
Dx(2,:) = 1;
end
--
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