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Why do the shape of finite elements matter?

I have used FEA for a couple of years now, but using it and using it correctly are two different things, safety factor is not the solution to everything. I have the feeling I won't be using it right unless I have a clear answer to that question: I…
Mister Mystère
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Can I use an explicit time stepping scheme to determine numerically whether an ODE is stiff?

I have an ODE: $u'=-1000u+sin(t)$ $u(0)=-\frac{1}{1000001}$ I know that this particular ODE is stiff, analytically. I also know that if we use an explicit (forward) time stepping method (Euler, Runge-Kutta, Adams, etc.), the method should return…
Paul
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Which journals should I read to keep up on advances in solving PDEs numerically?

I solve a lot of PDEs numerically, but applied math isn't my field. I haven't picked up on which applied math journals I should read to keep up with recent developments in the field. What are good journals to read to keep up with recent developments…
Dan
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Which novel data structures are used in adaptive FEM?

A lot of adaptive FEM libraries use more advanced mesh data structures to handle adding/removing nodes, edges, triangles, tetrahedra, etc. For example, the p4est library uses octree data structures for adaptive mesh refinement; you wouldn't often…
Daniel Shapero
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Linear programming with matrix constraints

I have an optimization problem that looks like the following $$ \begin{array}{rl} \min_{J,B} & \sum_{ij} |J_{ij}|\\ \textrm{s.t.} & MJ + BY =X \end{array} $$ Here, my variables are matrices $J$ and $B$, but the entire problem is still a linear…
Justin Solomon
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Sort of problems where SOR is faster than Gauss-Seidel?

Is there any simple rule of thumb to say if it is worth to do SOR instead of Gauss-Seidel? ( and possible way how to estimate realxation parameter $\omega$) I mean just by looking on the matrix, or knowledge of particular problem the matrix…
Prokop Hapala
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full rank update to cholesky decomposition

Let $A$ be a real, symmetric, positive definite matrix. It has at least 500 rows, possibly much more. I compute its Cholesky decomposition, which allows me to calculate $det(A)$ $A^{-1}X$ for some vector/matrix $X$ $A^{-1}$ (I am aware of the…
yannick
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Drawing samples from a finite mixture of normal distributions?

After some Bayesian update steps, I am left with a posterior distribution of the form of a mixture of normal distributions,$$\Pr(\theta| \text{data} ) = \sum_{i=1}^k w_i N(\mu_i, \sigma^2).$$ That is, the parameter $\theta$ is drawn from a…
Chris Granade
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Could you give examples of serious usage of meshfree methods?

I would like to hear about scientific codes and commercial packages utilizing meshless methods like Element-Free Galerkin based on Moving Least Squares functions. By "serious" I mean they could be used to solve problems comparable e.g. in size to…
vehsakul
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Which Sparse Matrix Solver Libraries can I run on Android?

The title says most of it. I'm looking for a lightweight and easy-to-use library that I can use for Android (NDK) projects. For dense stuff I like using Eigen but I haven't found many comprehensive (and documented!) libraries for sparse stuff that…
rsp1984
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suggestion for managing simulation runs?

This questions may be a bit off-topic in comp-sci. if it is needed please suggest where does it fit with. The question is regarding on how to manage all the simulation runs efficiently. let's say, for instance, a simulation requires fixing 2…
Chenming Zhang
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Schrodinger equation with periodic boundary conditions

I have a couple of questions regarding the following: I am trying to solve the Schrodinger equation in 1D using the crank nicolson discretization followed by inverting the resulting tridiagonal matrix. My problem has now evolved into a problem with…
WiFO215
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Which fourier series is needed to solve a 2D poisson problem with mixed boundary conditions using Fast Fourier Transform?

I have heard that a fast fourier transform can be used to solve the poisson problem when the boundary conditions are all one type... Sine series for dirichlet, cosine for neumann, and both for periodic. Considering a 2D rectangular domain, suppose…
Paul
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Is there a good tutorial or textbook-like source on implementing ENO/WENO with limiters in one (and more than one) dimension?

I've inherited a finite volume code that does a second-order discretization of flux terms for a set of mixed parabolic-elliptic equations with discontinuous diffusion coefficients. The impression I get is that Discontinuous Galerkin (DG) methods are…
Geoff Oxberry
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Computation Effort of Algorithms

Consider the strictly convex unconstrained optimization problem $\mathcal{O} := \min_{x \in \mathbb{R}^n} f(x).$ Let $x_\text{opt}$ denote its unique minima and $x_0$ be a given initial approximation to $x_\text{opt}.$We will call a vector $x$ an…
Suresh
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