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Results tagged with finite-element-method
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user 36
Usage of the Finite Element Method embedded in NDSolve and details on the implementation of the fem in mathematica.
11
votes
What is NDSolve`FEM`*?
In answer to David's question in the comments to the answer, I examine the contents of
Names["*`*"]
with every release. You can find all sorts of goodies this way. In addition to the FEM stuff, y …
- 32.6k
20
votes
How do I solve a PDE with a strange boundary condition?
Using V10's new FEM functionality, this problem can be solved as follows
<< NDSolve`FEM`;
omega = ImplicitRegion[x^6 + y^4 <= 1, {x, y}];
mesh = ToElementMesh[omega,
"MaxCellMeasure" -> {"Area" -> …
- 32.6k
24
votes
Accepted
Numerically solving an inhomogeneous partial differential equation
Edit of July 10, 2014
As of V10, this equation can now be solved with a single, simple call to NDSolve:
y = NDSolveValue[{
r D[y[r, z], z, z] + D[y[r, z], r] + r D[y[r, z], r, r] == r y[r, z],
y …
- 32.6k
15
votes
Nonrectangular region for NDSolve
This problem can be easily solved using V10's new FEM functionality.
For concreteness, let's suppose we want to solve the heat equation
$$u_t - \Delta u = 0$$
over the region
$$\left\{(x,y): -1 \leq x …
- 32.6k
7
votes
Speed of ConvexHullMesh
Quadratic?
randpt[n_] := Module[{prept = RandomVariate[NormalDistribution[], 3]},
prept/Norm[prept]];
experiment[n_] := First[AbsoluteTiming[ConvexHullMesh[Table[randpt[3], {n}]];]];
ListPlot[expe …
- 32.6k
67
votes
Accepted
Numerically solving Helmholtz equation in 2D for arbitrary shapes
I've encapsulated the code of the mysterious user21 into a helmholzSolve command. The code is at the end of this post. It adds very little to user21's code but it does allow us to examine multiple ex …
- 32.6k