Linked Questions

64
votes
4answers
4k views

Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?

Given a closed curve $\mathcal C$ in three dimensions, is it possible to use Mathematica's built-in functionality to compute a minimal surface whose boundary is $\mathcal C$? For simplicity, let us ...
38
votes
5answers
3k views

How to estimate geodesics on discrete surfaces?

Continuing with my interest on curvature of discrete surfaces here and here, I would like to also calculate and plot geodesics on discretised (triangulated) surfaces. Basically, my long-term idea ...
52
votes
2answers
2k views

A geometric multigrid solver for Mathematica?

Cross posted to community.wolfram.com Mathematica ships a variety of linear solvers through the interface LinearSolve[A, b, Method -> method] the most ...
19
votes
4answers
886 views

How to apply different equations to different parts of a geometry in PDE?

I want to solve two coupled partial differential equations on two dimension. There are two variables v and m. The geometry is a ...
27
votes
2answers
956 views

Smoothing 3D contours as post processing

Context Following this question (and great answer!), It would be nice to have a function which also smooths 3D contours plots once they have been done. There are various solutions which involve ...
22
votes
1answer
954 views

Implement fractional Laplacian

What is a way to implement the Fractional Laplacian with Mathematica? How can we apply such implementation to numerically solve the problem $$(-\Delta)^su = 1 \text{ in } B_1(0), \\ u = 0 \text{ in ...
10
votes
2answers
1k views

2D inhomogeneous biharmonic equation

How to solve a 2D inhomogeneous biharmonic equation with NDSolve? I tried the following code: ...
11
votes
2answers
572 views

Solving Cahn-Hilliard equation: LinearSolve: Linear equation encountered that has no solution

I have built the Cahn-Hilliard Eqs. in MMA (Mixed Formulation, second order), However, it doesnot work in MMA using Finite Element. LinearSolve: Linear equation encountered that has no solution. And ...
14
votes
1answer
2k views

Frequency domain Maxwell equations with PML boundary conditions

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
9
votes
1answer
885 views

Why should the spatial derivative order of the ODE *not* exceed two?

Following this question I came across this strange behaviour. Let me define a 1 D interval implicitely ...
7
votes
1answer
341 views

The rectangular region composed of two triangular regions contains a pde connecting the bc of the first and the second kind

I'm going to solve the Laplacian equation of the electrostatic field, which consists of two triangular regions, a rectangular region, a square, and on the intersection of the two regions of $$y=x$$, ...
2
votes
2answers
162 views

what causes the error “The dependent variable in the boundary condition needs to be linear” when using NDSolve?

V 12.1.1 on windows 10 Why the following works ...
4
votes
1answer
82 views

Strange behaviour in ToElementMesh

Why would that not work: ...