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2
votes
2answers
102 views

How does an automaton actually “compute”?

In my studies in computability I have come across the notion of the "machine", an abstract representation of a device that essentially computes. I have read about Turing Machines and Wolfram's binary ...
1
vote
2answers
2k views

Sparse Matrix Library for GPU

Anyone knows a good library which implements basic sparse matrix operations such as transpose, SpMV eigenvalues etc. in GPU (cuda/opencl) . Thanks
12
votes
2answers
4k views

Strategies for Newton's Method when the Jacobian at the solution is singular

I'm trying to solve the following system of equations for the variables $P,x_1$ and $x_2$ (all else are constants): $$\frac{A(1-P)}{2}-k_1x_1=0 \\ \frac{AP}{2}-k_2x_2=0 \\ \frac{(1-P)(r_1+x_1)^4}{L_1}...
3
votes
4answers
2k views

Heat equation (steady state) with boundary conditions at domain edges and inside the domain

I'm trying to solve the steady state of a heat equation problem in 2D $\Delta u = 0$ (3D also), with the method of solving the huge system of equations that arises from the discretization of the ...
3
votes
1answer
85 views

Improve optimization over 'mapping' of indices

I have two tables at my disposal, one work dataset and one reference dataset. Each dataset has got two columns, lets say these are fields A and B. I would like to associate the rows in the reference ...
5
votes
1answer
278 views

Recommendation for a python book for data processing

I've been doing FORTRAN programming for 10 years and I've started using python for a few years now, mostly for data processing. I've been lucky enough to work with people that are knowledgeable ...
13
votes
3answers
9k views

Understanding the “rate of convergence” for iterative methods

According to Wikipedia the rate of convergence is expressed as a specific ratio of vector norms. I'm trying to understand the difference between "linear" and "quadratic" rates, at different points of ...
4
votes
2answers
648 views

Orthonormalized Bernstein polynomials using Gram-Schmidt

I was wondering, before trying to do that myself, has anyone attempted to do orthonormalization of Bernstein polynomials using Gram-Schmidt? I discussed this with several people and have been told ...
1
vote
2answers
376 views

Checking for error in conjugate gradient algorithm

What is a good way to check if the any numerical error is occured in conjugate gradient algorithm. Additionally why is it not suggested to check error by checking A-orthogonality of search direction ...
8
votes
3answers
564 views

Evaluating sine and cosine of an integer multiple of an angle

When evaluating cylindrical harmonics, one needs to evaluate trigonometric functions $\cos(m\theta)$ and $\sin(m\theta)$, potentially for large integer $m$ and $\theta\in[-\pi,\pi]$. What is the best ...
5
votes
1answer
2k views

Magma vs. Plasma

I'm having a difficult time understanding the difference between the linear algebra packages MAGMA and PLASMA from just a quick glance. It looks like MAGMA is oriented towards GPU's and vector ...
1
vote
1answer
487 views

How to apply a Galerkin finite element method to a linear, one-dimensional boundary value problem

I have the following boundary value problem: $$-(\alpha u')' + \gamma u = f $$ in $\Omega = (a,b)$ with b.c. $u(a) = u(b) = 0$ and $\alpha > 0, \gamma ≥ 0$ and $f:(a,b) \to \Re $ The weak ...
6
votes
1answer
2k views

Flexible Mesh Framework

I am looking for flexible and easy to learn mesh framework which provides data structure for representing and manipulating meshes in 2D i 3D. I've already found a few: MSTK https://software.lanl.gov/...
9
votes
1answer
258 views

Hybrid spatial schemes for CFD: any downside to blending versus switching?

Aside from extra computational cost due to having to compute both fluxes over a certain region, is there any downside to blend two flux evaluations for a hybrid scheme in a finite volume method? The ...
4
votes
1answer
116 views

Simple substitutions using symbolic computing in MATLAB

Suppose I have the following MATLAB code. syms a b c1 c2 c1 = a + b + pi*b c2 = a + b + 0.5*b Then c1 gets evaluated to ...
7
votes
1answer
610 views

Decreasing spectral radius

I have a $4\times 4$ matrix and I want to use Jacobi iteration on it. Right now the spectral radius is higher than $1$. I know that the method is guaranteed to converge if the matrix is diagonally ...
11
votes
2answers
399 views

Computation of Cholesky factor

So the Cholesky decomposition theorem states that that any real symmetric positive-definite matrix $M$ has a Cholesky decomposition $M= LL^\top$ where $L$ is a lower triangular matrix. Given $M$, ...
5
votes
1answer
287 views

How to design good finite difference schemes? [closed]

In principle, I know finite differences. In university, we discussed it and derived consistency and boundary conditions. But I am still left with a big question. How to design a good finite ...
1
vote
2answers
121 views

how to approach time zero when the equation is not defined at that point

Some background: define a process $Y_t=\frac{1}{t}\int_0^tX_sds$, where $X_t$ is a standard Brownian motion. Then I define a function $u(t,X_t,Y_t)$ and require it to be a martingale. Thus, by ...
12
votes
2answers
978 views

What are some good data-types for unstructured cell-centered FVM CFD code?

I'm interested in an advice for efficient data structures for cell browsing in unstructured cell-based finite volume CFD. One example that I encountered (in dolfyn cfd code) goes like this (I'll show ...
12
votes
2answers
856 views

Numerical Integration - handling NaNs (C / Fortran)

I am dealing with a tricky integral that exhibits NaNs at certain values near zero and at the moment I am dealing with them quite crudely using an ISNAN statement which sets the integrand to zero when ...
5
votes
1answer
538 views

Poisson solver on unstructured mesh

For the 2D Poisson equation, there exist on finite difference mesh, some code taking $O(n \log(n))$ operations to solve it on a mesh with $n$ nodes. They rely on Fast Fourier Transform or Block Cyclic ...
11
votes
3answers
6k views

I am looking for a parallel dynamic graph library in C++

Hello scicomp community, I have worked in the area of graph algorithms using frameworks such as NetworkX (Python), JUNG and YFiles (Java). I am now entering the area of parallel and high perfomance ...
2
votes
1answer
217 views

$k$-Nearest Neighbor Search using examples

I want to perform $k$-Nearest Neighbor Search in multidimensional space, but not using for example $L_2$-distance. I want the user to specify some "similar"-pairs examples and then perform a search ...
3
votes
0answers
344 views

Orthogonal vs general curvilinear coordinates

Solutions to PDEs over irregular domains can be computed using the finite difference method by the introduction of so called body fitted coordinate systems where the coordinate lines are aligned to ...
6
votes
3answers
351 views

Computing an orthogonal matrix subject to linear constraints

I am looking for a method to solve the matrix equation $$ DXa = Xb $$ where $D\in \mathbb{R}^{n\times n}$ is diagonal, $a, b\in \mathbb{R}^{n}$ and $X$ is the unknown orthogonal $n\times n$ matrix ...
5
votes
2answers
209 views

Imposing invertibility on a Matrix

I have a symmetric positive semidefinite covariance matrix $A$, which is approximately computed as the output of a quadratic regression. I then need to invert $A$, but often it is close to singular. I'...
3
votes
1answer
676 views

minimization with orthogonality constraint

For positive semi-definite symmetric matrices $A,B$, how can I find an $X$ that minimizes $\text{Trace}(AX^TBX$) under the constraint: that $X$ is orthogonal. All the matrices have real entries and $...
1
vote
1answer
137 views

Calculating AIC (in R or any other statistical software)

I am trying to fit the log-log plot of the cumulative distribution of a network to one of three models: Exponential (EXP) ($P(k)\sim e^{-ak}$), Exponentially truncated power law (TRU) ($P(k)\sim k^{a-...
5
votes
2answers
310 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 ...
8
votes
1answer
262 views

Rebinning algorithm in VEGAS

I am trying to understand the rebinning algorithm of the VEGAS (original publication (preprint from LKlevin) and implementation notes) Monte Carlo integration. I will try to explain first what I think ...
3
votes
2answers
115 views

Are matlab C library versions backwards compatible?

I have some C++ code that links to matlab2008b. Are matlab 2012a and 2012b backwards compatible with 2008b? If it's not trivially compatible, are there some simple steps to make it compatible?
5
votes
1answer
3k views

Laplace's equation problem in Polar Coordinates (Edit)

Is there public code in Matlab for solving the Laplace equation in polar coordinates in a circular domain? I tried a lot but my level of Matlab and Mathematica is not good enough, but still not ...
5
votes
2answers
1k views

How to find all complex roots of an equation in a domain

I am facing a problem where I want to find the complex roots of $f(z)=z-sin(z)=0$ numerically. There are infinitely many roots of the function, but I am only interested in the $N$ closest to the ...
16
votes
7answers
1k views

Does Computational Science involve programming?

I read about computational science on Wikipedia, but my understanding is not very clear. Does computational science involve programming? How different is computational science from computational ...
1
vote
1answer
92 views

Existence of a solution at a stationary equation for quadratics

Given a convex quadratic function $f(x)$, to obtain a solution for which $f(x)$ has minimal value one sets $\nabla f(x)=0$, and solves for $x$. Suppose that the result of differentiation of convex ...
5
votes
2answers
148 views

What is the algorithm for computing block reflectors in xDLARFB

The theory behind computing a single Householder reflector to zero out part of a column of a matrix is pretty well described in Matrix Computations by Golub and Van Loan. However, the blocked ...
11
votes
3answers
522 views

Regression testing of chaotic numerical models

When we have a numerical model that represents a real physical system, and that exhibits chaos (e.g. fluid dynamics models, climate models), how can we know that the model is performing as it should? ...
6
votes
2answers
685 views

Implementing a numerical method for unconstrained optimization in Go

I would like to implement a Numerical Optimizer in my favorite language Go. It shall find solution(s) to this problem: maximize a function f(x) where ...
5
votes
1answer
1k views

Mixed boundary conditions Finite Element Method

I have the following problem in Finite Element Method $$ -(\alpha u')' + \beta u' + \gamma u = f$$ with $ \Omega = (0, 1)$, $ u(0) = 0 $ and $ u'(1) = 3 $ to be able to write the weak formulation ...
4
votes
1answer
207 views

Mesh partitioner that assures non empty subdomain?

Does some of you know a mesh partitioner that assures non empty subdomains? For METIS, ParMETIS and Zoltan this is not the case.
2
votes
1answer
388 views

rate of convergence for the second order accurate method on two dimensional grid

I am solving $u_t=u_{xx}+u_{yy}$ with a solver which is locally $O(dx^2+dy^2+dt^2)$. I use the following norm for the error between the numerical vector solution and the analytical solution $$||e||_2=\...
4
votes
3answers
154 views

Offline (visualisation) rendering in scientific computing

I need to simulate the movement of a large number of agents. The processes that govern the agents' movement are complex and so the entire process requires parallelisation. The output from this ...
3
votes
1answer
5k views

In Comsol Multiphysics, is there a way to change parameter values when something happens in the solution?

I'm beginning to learn Comsol Multiphysics as part of a modelling course in my masters degree. Currently, we are modelling a circuit with a spark gap, which presents some problems for me. I'm using ...
7
votes
3answers
3k views

What is the criteria for switching between Strassen's and Regular matrix multiplication Algorithms

Strassen’s Matrix Multiplication algorithm has theoretical performance of $ O( n^{log_2 7}) $. Regular MM algorithm has performance of $ O( n^{3}) $. At certain sizes of matrices (lets call it $n*n$),...
2
votes
1answer
296 views

Partitioning of mesh with 20 noded hexahedral elements [closed]

Is there a way to partition a mesh consisting of 20 noded hexahedral elements for parallel processing? I used METIS for partitioning mesh with 8 noded hexahedron elmements, which works fine but i don'...
3
votes
2answers
115 views

Representing an integral as a special function

In my research I have come across the following integral \begin{equation} f = \int_0^{2\pi} \text{d}\theta \exp\left\{\frac{3}{2}(h_1 \cos^2\theta + h_2 \sin^2\theta + 2 h_{12} \sin\theta \cos\theta)\...
7
votes
1answer
428 views

Numerical method for nonlinear system of algebraic equations of special type

I have a nonlinear system of algebraic equations of special kind: $$ \begin{array}{rcl} x_{i}+y_{i}+z_{0,1}+c_{i,1}z_{1,1} & = & d_{i,1}, \\ x_{i}^2 + y_{i}^2 + z_{0,2} + c_{i,1} z_{...
4
votes
1answer
100 views

Bounded Variation Spaces

Could someone explain me (roughly) the interest of Bounded Variation (BV) Spaces for PDEs ? Is there any numerical application of those space to real problems or is it just a theoretic way to ...
2
votes
1answer
93 views

Cholesky Algorithm loop-Carried

I would like to know how to unroll loop-carried dependency inside the cholesky algorithm. What are the techniques that I should know to accomplish this work? I need to know it because I want to ...

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