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Angular Velocity by Vector - 2D

This is originally a problem in programming, but since almost no one on Stackoverflow know how to solve this I went here instead; https://stackoverflow.com/questions/23003612/javascript-angular-...
308 views

FEM on tet10 element: negetive determinant at the Gauss point

I am trying to implement a fem code on tet10 elements. I follow the lecture notes for tet10 implementation given in http://www.colorado.edu/engineering/CAS/courses.d/AFEM.d/AFEM.Ch10.d/AFEM.Ch10.pdf ...
223 views

Calculate inverse of dense matrix with entries of very different magnitude

I need to calculate the inverse of a dense matrix, with some elements taking values as high as 1e9 and some around 1e2. What would be the best method to do it? Note: I am more concerned about the ...
133 views

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For software submitted to ACM TOMS, how does the ACM software license agreement interact with other licenses?

The journal Association for Computing Machinery Transactions on Mathematical Software (ACM TOMS) publishes many articles on numerical algorithms that include software implementations. According to ...
207 views

How should I report profiling/timing information about my code?

I've seen a lot of publications in Computational Physics journals use different metrics for the performance of their code. Especially for GPGPU code, there seems to be a great variety of timing ...
1k views

Shortley-Weller finite difference method

can you give me a link for a good and simple explanation of the Shortley-Weller finite-difference scheme? I tried to google it but all I get is (inaccessible) academic publications. I also tried ...
496 views

C - OpenMP, MPI, Serial Program

I'm part of a Computational Science course and come from a non-programming background, so please forgive me my ignorance. I'm working on a set of code in C to numerically solve the Navier Stokes ...
250 views

How to avoid overflow error in program that computes product of two numbers, such that when one is big enough to cause overflow, other is $0$?

Let us say that I have a function like so: def f(x): return g(x)*h(x) Now, g(x) and ...
4k views

How to find QR decomposition of a rectangular matrix in overdetermined linear system solution?

While trying to find cell-centered gradients in finite volume method computation of incompressible fluid flow I get over-determined linear system. This is a well known "cell based least-square" ...
474 views

What does symmetrize mean? (imposing multifreedom constraints to stiffness matrix)

I have a small FEM implementation program. And I want to add imposing multifreedom constraints (MFC) feature to it. The theory of master-slave method is given here (page 10 for general case). ...
485 views

Perturbation of Cholesky decomposition for matrix inversion

I am looking for a computationally cheap way to compute $x$ such that $$(L L^T + \mu^2 I)x = y$$ where $L \in \mathbb{R}^{n \times n}$ is a lower triangular definite positive matrix (with some very ...
3k views

Discrete Poisson Equation with Pure Neumann Boundary Conditions

I'm trying to implement the Helmholtz-Hodge Decomposition in 2D, which states that a vector field is composed by a rotational free component, a divergence free component and a harmonic component. ...
280 views

Approximating and visualizing basins of attraction

I am working on estimating the position and orientation (pose) of a model (rigid object) from its silhouette in an image. For this, I have constructed an error measure between the model in its pose ...
90 views

Linear programming boundedness

Assume the optimal value of a primal problem is bounded. Is the following statement true? If the primal problem is bounded, then its dual problem is bounded as well.
437 views

LU Decomposition of PSD Matrix + Diagonal Matrix

If I have a psd, symmetric matrix $\mathbf{A}$ and I need to do LU decomps on $\mathbf{B_i}= \mathbf{A} + \mathbf{D_i}$ (where $\mathbf{D_i}$ is a diagonal psd matrix, where $\mathbf{D_i}$ changes ...
204 views

Is there a minimum angle requirement for cells in the finite volume method?

In his talk "What is a good linear finite element?", Shewchuk states that small dihedral angles in linear tetrahedra elements cause ill-conditioning of the stiffness matrix. Do small dihedral angles ...
2k views

Partial trace algorithm (original)

In general, is there a partial trace algorithm (ideally for systems of any size) that can be coded using basic matrix operations found in software like Mathematica or Maple? All of the methods I'm ...
250 views

Interpolating a mathematical function using a Hermite Cubic Finite Element Space

I have a Hermite Cubic Finite Element Space on a computer in the form of Matlab m-files. More specifically, I can evaluate four "shape functions" $N_1, N_2, N_3,$ and $N_4$, for which the following ...
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DST using FFT routine

Please can you help me with my problem? On Wikipedia, in article Discrete sine transform, this is written (chapter Computation): "Although the direct application of these formulas would require O(N2) ...
295 views

Finite Elements Weak Formulation generalization

I am struggling with an equation that represents the Weak form of Galerkin method: \$ \phi^{T}F(\textbf{u})\sim \int_{\Omega}^{ } \phi.f_{0}(\mathit{u},\nabla \mathit{u}) + \nabla\phi:f_{1}(\mathit{u},...
4k views

Why a finite difference scheme would give second order of accuracy in norm L2 but 1.5 with L1 (while 1 with Linf)?

My finite difference scheme for the 2D Euler equations is second order accurate in theory, since all the terms are second order accurate, with the advective terms being third order. So I expect a rate ...
1k views

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Interpolation of function onto mesh gives different results, depending on mesh density

I wanted to test the numerical accuracy of my program. For that I wanted to interpolate the function $$f=I_0\exp\left(-100x^2\right)\exp(-100y^2)$$ onto a grid, defined on $$\Omega=[0,1]^2$$ by using ...
31k views

What are the conceptual differences between the finite element and finite volume method?

There is an obvious difference between finite difference and the finite volume method (moving from point definition of the equations to integral averages over cells). But I find FEM and FVM to be very ...
8k views

How mature is the “Julia” scientific computing language project?

I'm considering learning a new language to use for numerical/simulation modelling projects, as a (partial) replacement for the C++ and Python that I currently use. I came across Julia, which sounds ...
1k views

Scientific standards for numerical errors

In my field of research the specification of experimental errors is commonly accepted and publications which fail to provide them are highly criticized. At the same time I often find that results of ...
3k views

What attributes make a figure “professional-quality”?

I've heard people say that plots produced by ORIGIN tend to look polished and "professional," whereas plots produced by Mathematica do not. However, most plot-creation programs are quite configurable ...
7k views

Mathematical Libraries for OpenCL?

I am looking for information from anyone that has tried to use OpenCL in their scientific code. Has anyone tried (recently) ViennaCL? If so, how does it compare to cusp? What about OCLTools? Does it ...