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7
votes
2answers
136 views

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 ...
11
votes
1answer
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 $F(y)$ ...
3
votes
1answer
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 ...
0
votes
1answer
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?
7
votes
1answer
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 ...
4
votes
2answers
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 ...
4
votes
3answers
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 ...
9
votes
1answer
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&...
1
vote
1answer
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 ...
2
votes
1answer
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 ...
3
votes
1answer
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 ...
2
votes
1answer
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 ...
0
votes
1answer
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 ...
2
votes
1answer
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 ...
5
votes
3answers
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 ...
5
votes
1answer
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) ...
11
votes
3answers
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 ...
1
vote
1answer
6k views

Numerically determining convergence order of Euler's method

I need to numerically determine the convergence order of Euler's method for various step-sizes. I am unsure how to go about doing this. Here is the question: Problem statement: $\frac{dy}{dt}=\alpha ...
4
votes
1answer
400 views

PETSc input format for linear solvers

I’m going through some considerable effort to translate one of my codes from MATLAB. It’s a type of finite element code and I haven’t implemented the solver yet but comparing CPU times for simply ...
1
vote
1answer
1k views

Returning variable length arrays in OpenCL

I'm new to opencl and I'm trying to figure out how to return a variable length array of numbers. (I'm using Cloo for C# .net) I am doing image processing and I've written a program to look for ...
3
votes
1answer
305 views

Sparse linear solvers in C?

I'm working on translating a discontinuous Galerkin code from MATLAB to C and I'm at the final point where I need to solve a sparse system. I've taken a course in C before but I'm very rusty and wasn'...
3
votes
2answers
3k views

Matlab preconditioned conjugate gradient on big matrix

I have a sparse $5\,656\,236 * 5\,656\,236$ matrix $A$ with $166\,526\,888$ non-zero elements. The matrix comes from using the finite element method on a linear elasticity problem and is positive semi-...
1
vote
2answers
102 views

Clustering algorithm for a data set with at most N clusters

I have a data set that I'm trying to cluster, and I know that there will be at most N clusters (based on some physical properties of the thing the data set represents). However, there could be as few ...
1
vote
1answer
57 views

Searching in a large dataset

I am working on a model of social interactions in mice. I have mice and boxes and a simulation that outputs which mouse stays in which box during which time period (this comes out as a mouse is ...
0
votes
1answer
784 views

sparse matrix format with fast row and column access

Is there an efficient storage format for general, non-symmetric sparse matrices for which one can find all non-zero entries in a given row or column in $O(d)$ time? ($d$ is the max number of non-zero ...
3
votes
2answers
2k views

Fractional-step method

I am about to start my journey into the world of CFD and wanted to start with the Fractional-step method for solving the incompressible Navier-Stokes equations. Could you perhaps suggest some articles ...
0
votes
1answer
66 views

Can I use Engineering codes like ASHRAE , NFPA and UPC in my software without permission? [closed]

Say, I want to use the UPC code Water Supply Fixture Unit tables in my software that I'm writing ... is it okay or there will be copyright issues?
2
votes
0answers
732 views

How to solve global equation in Comsol only once? [closed]

Let's assume that I have a comsol model for solving time-dependent problem. In order to find initial value for one variable I need to solve simple algebraic equation before starting simulation, ...
3
votes
2answers
370 views

Finite element stabilization schemes for incompressible flow

I am looking for an easy to implement stabilization scheme that can be used with equal order ($P_1-P_1$ or $Q_1-Q_1$) finite elements for fluid flow. Is there something like this or should I stick to ...
3
votes
1answer
443 views

Linear Algebra / Numerical Solution Of Matrix With Nullspace

I have a question relating to linear algebra. We have a fluid solver that solves the poisson equation for pressures. When there are areas of the domain that are entirely enclosed by Neumann ...
11
votes
4answers
13k views

Fastest PCA algorithm for high-dimensional data

I would like to perform a PCA on a dataset composed of approximately 40 000 samples, each sample displaying about 10 000 features. Using Matlab princomp function consistently takes over half an hour ...
3
votes
1answer
170 views

What is the most efficient way to represent a 1D function using $hp$-finite element basis functions

Given a one-dimensional function (let's say infinitely differentiable) and a prescribed accuracy of an L2 (or H1) norm, what is the optimal mesh and (in general arbitrary) polynomial orders on each ...
3
votes
2answers
304 views

openmp update matrix from neighboring elements (parallelise preconditioner)

Issue of data dependency with stencil code... How to parallelise this using openmp? I looked at the openmp manual, I figured out how to use DO ORDERED to get the same result as the serial version, ...
7
votes
3answers
3k views

Algorithm to compare two large sets

I am a novice in the world of algorithms, ignorant of the taxonomy used.Please pardon me. I have two large sets of numbers A and B where A = {x| 0< x< 9999999999 } B= {y | 0 < y < ...
0
votes
1answer
238 views

Implementation of the MARTINI force field

Given an input parameters for the MARTINI force field such as: ...
7
votes
2answers
1k views

What are some of the differences between using a Lagrangian and Eulerian framework to quantify passive scalar dynamics?

On one hand, one may seed the domain with particles and track their trajectories in the Lagrangian sense by implementing a Lagrangian particle tracking model. On the other hand, one may use the ...
4
votes
1answer
144 views

Solver for eigensystem of vectors?

I'm trying to solve a multipole system. It involves a matrix of 3x3 tensors $A_{ij}$ and a vector of 3-tuples $\mathbf v_i$. $$\left(\begin{matrix} A_{11} & A_{12} & \cdots & A_{1n}\\ A_{...
6
votes
1answer
92 views

Numerical iterative method, estimating error

Given iterative method: $x_{n+1}=0.7\sin x_n +5 = \phi(x_n)$ for finding solution for $x=0.7\sin x +5$, I want to estimate $|e_6|=|x_6-r|$ as good as possible, with $x_0=5$, where $r$ is exact ...
8
votes
1answer
1k views

Why am I getting so much error for my Runge Kutta Fehlberg solver?

My current project is a reprogramming of a protein folding model involving the solution of thousands of ODEs in C++. I've been making some stop and start progress as I'm writing the solver to run ...
5
votes
1answer
570 views

Riemann Solver in WENO methods

I'm reading now Shu, C.-W. (1999). High Order ENO and WENO Schemes for Computational Fluid >Dynamics. (T. J. Barth & H. Deconinck, Eds.)Lecture Notes in Computational >Science and Engineering, ...
0
votes
1answer
171 views

Neighbor pattern look-up table enumeration on an octree mesh

I am working with an octree mesh where variables are stored in a collocated fashion at octant centers. I want to construct a lookup table for interpolation weights that may occur using only a cell and ...
3
votes
1answer
241 views

Inverting many small matrices in parallel

I am trying to find a good way to handle the following problem: Let C be an N by 3 array (corresponding to points in $\mathbb{R}^3$). There is a method I am interested in testing which requires ...
6
votes
3answers
142 views

Newton's method for a given polynomial

Let $f(x)=\frac{1}{5}x^5+\frac{1}{3}x^3+x-1$ Show that $f$ has only one zero $r$ in interval $(0,1)$ To find approximation of $r$ we apply Newton's method $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}...
4
votes
1answer
3k views

How to integrate numerically over a radial domain

I want to integrate a function over a radial domain $D=\{r<r(\theta)\}$. The change to polar coordinates yields: $$ \int_D f = \int_0^{2\pi} \int_0^{r(\theta)}f(r,\theta)rdr d\theta $$ so I tried ...
6
votes
1answer
12k views

Concave polygon 'hull' finding

I implemented an algorithm to find the alpha shape of a set of points. The alpha shape is a concave hull for a set of points, whose shape depends on a parameter alpha deciding which points make up the ...
5
votes
1answer
927 views

Why dual graph for mesh partitioning

Software such as ParMetis or PTScotch partition a graph. When one wants to use it for mesh partitioning (for example for FEM), a dual graph whose vertices represent cells of the original mesh is ...
7
votes
5answers
627 views

Recommended Route for Mastering Inverse PDE Problems

I would like to master Inverse PDE Problems particularly with the use of Finite Elements. My problem is I don't know where to start. Should I begin by reading a book on Inverse Problems or on PDE-...
4
votes
1answer
112 views

What is the added cost of generalizing an eigensystem?

Problem Let's say I can write a model as the Hermitian eigensystem: $$ A x = \lambda x $$ where $A \in \mathbb{C}^{n\times n}$ is Hermitian, or as the generalized Hermitian eigensystem: $$ \tilde A \...
3
votes
2answers
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++....
9
votes
1answer
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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