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1500 questions
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2 answers

How to use grid sizes that are not powers of two in Geometric Multigrid

I am trying to solving a poisson equation in structured grid with Geometric Multigrid method. However, when coarsening the fine grid, I simply double the grid spacing at each successive level. That means that the number of points on the finest…
Anyang
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Performance of kd-tree vs brute-force nearest neighbor search on GPU?

I wonder if there is any study that compares the performance of kd-tree vs brute-force nearest neighbor search on GPU. Post #4 on this page suggests that kd-tree may not be the optimal algorithm for GPU but I wonder if there is any data supporting…
sl1129
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objects in buckets -- assignment optimization problem

Let $B$ and $I$ denote finite sets, let $$ E: I \times B \to \mathbb{R}_{> 0} $$ be a function, and let $s_b \in \mathbb{N}$ for $b \in B$ be given. Find $x_{i, b} \in \{ 0, 1 \}$, for $b \in B$ and $i \in I$ maximizing $$ \sum_{i \in I} \sum_{b…
popstack
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Mesh ordering algorithms used by COMSOL Multiphysics

Ordering of elements in an unstructured mesh is undoubtedly very important for the performance of computations. For example, it determines the structure of sparse matrices arising from PDE discretizations, which affects the performance of most…
Jakub Klinkovský
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Discrete wave simulation - absorbing boundaries?

I wrote a simple 2D wave simulation using the following equations: $$\frac{\partial^2 u}{\partial t^2}=c^2\nabla^2u$$ Where $\nabla^2$ is the discrete laplace operator using a Von Neumann neighborhood lattice. $$\mathbf {D}^2_{xy} = \begin{bmatrix} …
Bloc97
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Recommendations for a usable, fast Java matrix library?

This complements an earlier question on usable, fast C++ matrix libraries. I've looked at the Java Matrix Benchmark, and it seems like the performance of java matrix libraries is all over the place. The Apache Commons Math library seems like a…
cjordan1
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What’s so great about derivative-free solvers for SDEs?

I am trying to familiarise myself with SDEs and have been reading a few review papers on the topic. They leave the impression that a great deal of work has been put into solvers that are derivative-free. To my understanding this means that for a DDE…
Wrzlprmft
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What is the origin of the spurious oscillations in the Crank-Nicolson scheme?

I was reading about the Crank-Nicolson method, and it is often said that it can produce "spurious oscillations" or that this method is prone to "ringing", especially for large time step and stiff initial value. I'm curious about that phenomena but I…
Matthieu
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C library - iterative sparse complex linear equation solver?

Where can I find a library to solve a sparse complex matrix equation iteratively in C. So far I've only found libraries for direct solution to complex systems, and libraries for iterative solutions to real systems, but no solvers for iterative…
LinearAlg
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testing derivative approximations

I'm writing a library that involves some approximations of variational calculus problems. Whenever I implement routines to evaluate the derivative or Hessian of an action functional $A$, I write a test to check that these are working correctly. To…
Daniel Shapero
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How can I derive the a priori error estimate for a symmetric bilinear form using lagrange finite elements?

Suppose that I'm solving the poisson equation by the finite element method by lagrange elements. I know that the error can be measured in a variety of ways, depending on which norm you choose. For a given lagrange element order p and a symmetric…
Paul
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Numerically stable computation of the Characteristic Polynomial of a matrix for Cayley-Hamilton Theorem

I was wondering if there is any known way to compute the Charactaristic Polynomial P of a matrix A numerically stable in the sense of realizing the Cayley-Hamilton Theorem, i.e. that P(A)=0. I've found and implemented a couple of ways, but when the…
Niv Hoffman
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reformulating inverse problem as multi-objective optimization

I'm working on an inverse problem for my Ph.D. research, for which I'll write the objective functional as $J(\theta) = E(G(\theta) - u^o)$, where $\theta$ are the parameters, $G$ is the forward map from parameters to observations, $u^o$ are the…
Daniel Shapero
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5 answers

Interpolate 2D data

I generated a cartesian grid in Python using NumPy's linspace and meshgrid, and I obtained some data over this 2D grid from an unknown function. I want to get an approximation of the value of the function over some points inside the boundaries of…
astrojuanlu
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How to handle large numbers of output data sets from a simulation/sensitivity analysis?

Somewhat related, but I think the question is distinct enough to justify a separate question. As a bit of background, I come from a observational/statistical Epidemiology background, working with data that's been collected already, so even our large…
Fomite
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