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Convergence of adaptive finite elements with inexact solves

I'm working on some adaptive discontinuous Galerkin codes for time harmonic wave propagation, currently just Helmholtz, but will be branching out once I have a working prototype in this case. There ...
992 views

Numerical methods for inverting integral transforms?

I'm trying to numerically invert the following integral transform: $$F(y) = \int_{0}^{\infty} y\exp{\left[-\frac{1}{2}(y^2 + x^2)\right]} I_0\left(xy\right)f(x)\;\mathrm{d}x$$ So for a given $F(y)$ ...
241 views

Can one use incompressible flow approximation for fluid flow in heated pipes?

I was wondering if the use of incompressible flow approximation for fluid flow in heated pipes is reasonable. A previous question (Definition of incompressible flow) seemed to focus on Natural ...
204 views

What libraries provide an implementation of multigrid?

I am working on numerical method of Multigrid. What's the available implementation(solver) (actually used in scientific computation) of multigrid method?
97 views

Shall I derandomize a randomized algorithm in real application?

In general (and in real application), suppose I am using a randomized algorithm (e.g. Use MCMC to sample from a distribution and then compute $E(f(x))$ for some function $f$) Assume my algorithm will ...
380 views

Can the Levenberg-Marquardt algorithm be used for minimization and not fitting

Can the Levenberg-Marquardt algorithm be used for minimization and not fitting? Usually we input the derivative of the function we want to fit in the minimizer. Now if I assume I have an objective ...
345 views

Is there a general framework for solving PDEs on uniform grid in parallel

Hej, I want to simulate a partial differential equation (a modified Cahn-Hilliard equation, but the details do not matter much. The questions also applies to the diffusion equation). I'm looking for ...
2k views

Solving system of linear equations with cyclic tridiagonal matrix

I have this problem in my textbook: Suggest efficient algorithm for solving system of linear equations with cyclic three-diagonal matrix, that is of the form: \begin{bmatrix} a_1&b_1&0&...
112 views

How to allocate memory for successive iterative solutions with potentially different non-zero structure?

Background I am solving the unsteady heat equation in 3D using an alternating direction implicit (ADI) method. This means that I am solving three different tridiagonal systems within a single timestep ...
129 views

Detect rigid body motions in a cloud of points

This question popped up today in our group meeting. Suppose you are given a cloud of N points in 2D and each is associated with a velocity vector. These points are associated with particles on a 2D ...
817 views

Sparse matrices that represent common stencil operations

I am not sure if this is the correct place to ask this question! Is there a data set such as the University of Florida Sparse Matrix Collection which is produced from stencil operations? Or is ...
156 views

Inclined plate capacitor grid/ mesh

You can calculate the electric potential over every point in a defined space by solving Laplace's equation. To do this in a computer program you set up an 2-d array/ matrix and loop the internal ...
112 views

max speed <--> time discretization

I'm working on a heat diffusion problem, $$\frac{\partial T}{\partial t}=\vec{\nabla}\cdot\left(\kappa T^{5/2}\,\vec{\nabla}T\right)$$ I know that, after discretization, the time step for the 1D ...
55 views

Algorithm to extract the decaying parts of complex exponentials

I have an oscillatory, decaying function that can be decomposed as $$\sum_k e^{iz_kt}$$where $z_k$ are complex. What I want is the imaginary parts of all of the $z_k$'s with some range of real ...
333 views

Machine epsilon does not limit relative rounding error for denormals. Is this a problem?

As we know, machine epsilon limits relative rounding error in the range of normalized floating point numbers. But it is easy to check that this is not true for denormalized numbers. My question is ...
276 views

Is is possible to mix finite-volume and finite-difference discretisations when solving a coupled non-linear system?

In my last question I noticed a peculiar error when solving the Poisson equation using finite volume method (FVM), Peculiar error when solving the Poisson equation on a non-uniform mesh (1D only) ...
1k views

Libraries for solving Lyapunov's equation

The following matrix equation $$B\Sigma + \Sigma B^T + C = 0$$ in $\Sigma$ $-$ for given $B$ and $C$ matrices $-$ appears in my work as a characterization of a covariance matrix. I have learned that ...
6k views

2k views

How Do I solve large systems given UMFPACK memory limitations?

I am trying to solve a system of equations (A x = b) for 3D heat diffusion (i.e. each equation has at most 7 terms not including the constant "b" term) using UMFPACK with boost numeric bindings to C++....
2k views

What does Static, Dynamic and Single Dynamic linking mean?

I use Intel MKL for BLAS and use the Intel MKL Link Line Advisor for help with the command line options. The advisor provides options for Static, Dynamic and Single Dynamic Library. What do these ...

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