0
votes
0answers
7 views

Am I using cyclic reduction to parallelize this algorithm?

I am attempting to implement a modified anisotropic-diffusion filter on the GPU. The methodology I describe here including the equations and code listing are taken from this paper . The author of ...
2
votes
2answers
64 views

Algorithms for radiation treatment planning

I have a medical physics problem - I want to maximise the dose absorbed by a brain tumour whilst minimising the dose in the rest of the brain, especially certain organs, such as the pituitary gland, ...
2
votes
0answers
17 views

How to Check a Hyper-Cube for Defects

I would greatly appreciate some help/references on solving the following problem: You are in charge of searching through a n-dimensional hyper-cube $[0,1]^n$ to make sure that it does not contain ...
1
vote
1answer
49 views

Direct or iterative solver for ill-conditioned problems

I have to solve an ill-conditioned sparse matrix. Once I read that iterative solver are the better tool for such problems. Is that true? If yes, why?
0
votes
0answers
14 views

Finding self-kissing points on a plane curve?

I have a curve in the complex plane given by $$ f(t) = \sum_k r_k\exp(2\pi\mathrm{i}(t+\varphi_k)p_k). $$ Some of the parameters are specially chosen: $r_k>0$, $\sum_k r_k=1$, $p_k\in\mathbb{Z}$, ...
0
votes
0answers
23 views

Problem solving on GPU / FPGA

I was just reading this paper (http://math.ipm.ac.ir/~tayfeh-r/papersandpreprints/h428.pdf) in it some algorithm found a solution to a problem within 12 hours on a cluster of sixteen 2.6 GHz PC. I was ...
0
votes
0answers
25 views

Help with the definition of constraints for a joint optimization problem

A trajectory is piecewise defined by the following polynomial form: $$ f(t) = a + bt+ct^{2}+dt^{3}+et^{4}+ft^{5}+gt^{6}+ht^{7}+it^{8}+jt^{9} $$ for every single segment composing the trajectory (the ...
0
votes
1answer
27 views

GAMS solvers: which one to use

The other day I had a discussion with a friend about the GAMS solvers and we were wondering what are the mathematical differences between the solvers. Which one to use for which kind of problem? How ...
0
votes
0answers
14 views

Is it possble to store a counter that could reach $\lfloor \frac{N}{x}\rfloor$ using $\lceil\log_2(N+1)\rceil$ - $\lfloor\log_2 x\rfloor$ bits? [on hold]

Let $x,N$ be positive integers. I'd like to store a counter which could reach value of $\lfloor \frac{N}{x}\rfloor$ (i.e. could take any value in $0,1,\ldots,\frac{N}{x}$) using ...
1
vote
1answer
29 views

Value of density when there are no or very few neighbours in SPH simulation

Sorry for the noob question. I am trying to implement SPH using the directions shown in this paper. The density needs to be updated using the formula The smoothing kernel is If there are no ...
0
votes
2answers
53 views

Manufactured solution for pressure based 3d incompressible Navier-Stokes solver with wall boundaries

I already successfully verified my solver (SIMPLE-type FVM-method) with the following manufactured solution (3d Taylor-Green vortex) on the solution domain $[-1,1]^3$ with Dirichlet boundary ...
2
votes
2answers
64 views

Find $\min x^TAy$ subject to $1^Tx=1^Ty=1,x\ge 0,y\ge 0$

In the following problem, $A$ is a given $\mathbb{R}^{m\times n}$ matrix: \begin{align} \mbox{minimize}\quad & x^TAy \\ \mbox{subject to}\quad & 1^Tx=1^Ty=1, \\ & x\ge 0,y\ge 0. ...
0
votes
1answer
39 views

Solving Initial Value problem ignoring the time-derivative

I am looking at a heat initial value problem \begin{align} \frac{\partial u}{\partial t}-\nabla^2u = f\quad&\text{in}\quad \Omega\times(0,T)\\ u = g \quad&\text{on}\quad ...
1
vote
1answer
40 views

Shared memory parallel computing solutions compared

As of 2015, what shared memory parallel computing solutions are available? What are the advantages and disadvantages of each for various use cases arising in high performance scientific computing? I ...
2
votes
1answer
36 views

What are the novel MOOP method?

As you know, the multi-objective optimization methods are developing so fast, i.e.,epsilon constraints. I have a problem that I want to apply the most recent MOOP method for it. Please tell me the ...
0
votes
1answer
20 views

Simulating a wavepacket

Basically I have the following equation of motion, for some wave packet $\mathcal{Q}(z,t)$: $$ \partial_t \mathcal{Q}(z,t) = f(z)\mathcal{Q}(z,t) + \int_{-\infty}^{\infty}\text{d} z' ...
1
vote
0answers
30 views

Library for calculating determinants with Kronecker products

I need to calculate a determinant consisting of vectors, using the Kronecker product as product. As an example I would need to be able to calculate: $\left| \begin{array}{cc} ...
0
votes
0answers
26 views

Elasticseach is not matching ”_id” between the clusters [on hold]

I have two Web Servers ws001 and ws002 working as load balance for Elasticseach and I am trying to catch/count the hits for a specific page which is something like this: mysite.com/listing/item-123/. ...
0
votes
0answers
15 views

Is there a standard for determining the accuracy of a polygon interpolation technique?

I'm looking into polygon interpolation, and was curious if there are any standards for determining the accuracy of polygon interpolation techniques. I've been looking through papers and lecturers ...
0
votes
0answers
44 views

Programming language for scientific computation [duplicate]

What programming language is best to learn for scientific computation? Fortran, C, Python?
2
votes
0answers
40 views

Laplacian discretization for parametric curves

I know how to compute the discrete Laplacian of a graph and of a mesh (the Laplace-Beltrami operator). Is there an analogous definition for the computation of the Laplacian of a parametric curve ? ...
3
votes
1answer
59 views

Visually appealing ways to plot singular vector fields with matplotlib or other foss tools

What is the best way to get a visual appealing plot of a singular vector field (if you want to visualize also the field strength). As an example I am playing with the electric fields of two point ...
0
votes
0answers
23 views

How to speed up calls to integral2 in matlab

I am performing a 2D integral for each time step of a calculation. The problem is that I need to vary through all possible permutations of a1,a2 (which always ...
3
votes
1answer
52 views

Simple way to derive transpose of a vectorized operation

In a program I'm writing, I have a sub-routine that does some vectorized linear operations (specifically differentiation). Say for convenience I have defined the following inline function, which ...
0
votes
0answers
18 views

Compare Sumatra and Biolite

I want a tool that can handle handle data provenance and record the following: Tools version State of machine-Linux,Java version Node PBS id,time stamp, who command I was reading about Biolite and ...
5
votes
2answers
86 views

How to impose boundary conditions on eigenfunction problems?

I am trying to solve for the eigenfunctions of a (1D) differential operator using finite differences: $$A \, f(x) = \lambda f(x)$$ Here is an example in Python where $A = \partial_x^4$: ...
1
vote
0answers
35 views

How to determine the minimum number of multiplication needed for a specific expression?

Is there any algorithm to determine the minimum number of multiplication(division) of a specific expression? and the optimal expression form for implementation? For example, given values of ...
1
vote
1answer
57 views

Discontinuous Galerkin, residual orthogonal to test functions?

I am a little confused about where does the mass and stiff matrix come from. In Discontinuous Galerkin we divide the domain in elements, $\Omega = \cup^K_{k=1} D^k$. Then assume the solution $u$ can ...
2
votes
1answer
42 views

Modified diffusion equation and unstabilities

I am trying to simulate the phase separation of a binary mixture. If the free energy F is known as a function of the concentration $c$, the dynamical equation is: $ \frac{\partial c(x,t)}{\partial ...
1
vote
1answer
50 views

Is it possible to eliminate the inner sum to evaluate numerically?

Any hints on how to simplify the following double sum to be able to find the sum at least numerically? $$\sum_{n=2}^{\infty}\frac1{n(n^2-1)} \sum_{k=1}^\infty \frac{(k-1/n)^{2n-2}}{(k+1/n)^{2n+2}}$$ ...
4
votes
2answers
56 views

Computation of multipole expansion of potential not converging

According to Beatson and Greengard's short course on FMM: ( Eq. 5.15 & 5.16 setting k=1, q=1 ) We can approximate a potential $\phi = 1/(r-R)$ using: $$ {1\over |\vec{r}-\vec{R}|} = ...
2
votes
1answer
40 views

Derivation of Adams-Bashforth coefficients

From the order condition $$\sigma(w)=\frac{\rho(w)}{\ln w}+O(|w-1|^p)$$ I get $$\sigma(w)=1+\frac{3}{2}(w-1)+\frac{5}{12}(w-1)^2=-\frac{1}{12}+\frac{2}{3}w+\frac{5}{12}w^2$$ Those coefficients are ...
0
votes
2answers
76 views

Solving a double integral in Matlab

I need to solve this integral: $M = \rho h \int_0^a \int_0^b N^2 \ dx dy$ where $N$ is defined as: $N = sin\left(\dfrac{\pi}{4}\eta +\dfrac{3\pi}{4}\right)sin\left(\dfrac{\pi}{4}\eta ...
0
votes
0answers
7 views

Which Basis Set is suitable For Mercury-complex in DFT calculations?

Which Basis Set is suitable For Mercury-complex in DFT calculations? Please provide the answers with any journal reference.
-1
votes
1answer
35 views

Nbody problem with stars and planets [on hold]

Which method is the most efficient to simulate an n-body problem in python? ie - runge-kutta, euler, verlett, etc
-2
votes
0answers
25 views

how could I find the minimum of computational cost of operation [on hold]

Let the following statement: $$\phi=p_{xx}A^{-1}B+2p_x(A_x^{-1}B+A^{-1}B_x)+p(A_{xx}^{-1}B+2A_x^{-1}B_x+A^{-1}B_{xx}),$$ where $$A_x^{-1}=-A^{-1}A_xA^{-1}$$ and ...
0
votes
0answers
35 views

Looking for Fluid Dynamics Interactive App [closed]

Do you know from any interactive software to learn/simulate basic Fluid Dynamics concepts? Like communicated vessels, Pascal and Bernoulli principles, etc. It would be great to learn by tweaking ...
0
votes
2answers
66 views

Faster methods for projecting a mesh onto a hierachally unrelated mesh?

I have a set of independent meshes whose results I would like to project onto another non-hierachally related mesh. Until now, I've been accomplishing this by finding the nearest-distance node in the ...
0
votes
0answers
27 views

Solving nested MILP problems

I want to solve a family of MILP problems (indexed by $k \geq 0$) of the following type: $$ \begin{align} \max \; c^Tx \;\; s.t. \\ Ax \leq b \\ d^Tx \leq k \end{align} $$ In other words, the ...
1
vote
0answers
42 views
+50

How can I run Normal Boundary Intersection (NBI) method with matlab or any other software?

I have a constraint optimization problem. I want to convert it to a multi-objective mathematical programming problem (so-called Multi-objective optimization , vector optimization). I need to run ...
3
votes
2answers
124 views

Initial Value Problem using Finite Element

I am trying to implement a FEM solver for the following initial value problem \begin{align} \frac{\partial u}{\partial t} - \nabla^2 u &= f\quad \text{ in } \Omega\times (0,T)\\ u &= g\quad ...
0
votes
0answers
27 views

Calculating Conditional Expectations

I would like to compute the conditional expectation of a particular function : $E_{t}\left[ R(A_{t+1}, \eta_{t+1})\right | A_t]$ where $A_{t+1}$ and $\eta_{t+1}$ are two rv correlated to each ...
0
votes
0answers
35 views

Convergence of a DASPK depending on DAE formulation

I have a system of non-linear DAE and I noticed that the system does not converge if some of the equations are not differentiated. For example, if the control volume equation is represented as this: ...
2
votes
0answers
60 views

Using SVD to biorthogonalize left and right eigenvectors?

I have a set of left and right eigenvectors from an nonsymmetric eigenproblem, and I'd like to biorthogonalize them. I tried Gram-Schmidt, but this fails for most cases. I then read that the SVD is ...
1
vote
3answers
127 views

Algorithm to compute the intersection of two lines given their cartesian equations

I'm looking for a way to compute the coordinates of the intersection of two lines. Each lines are defined with a point and a normal vector. We can assume than the normal vectors are not zero and ...
0
votes
0answers
29 views

quick projection

I am using level method to solve non-smooth convex programming problem (where the objective function is given by an oracle from another program ): http://www2.isye.gatech.edu/~nemirovs/Lect_EMCO.pdf ...
3
votes
1answer
89 views

Converting quadratic constraint to linear matrix inequality

So I have the quadratic programming problem: (x is the variable) $$\text{Minimize}\;\; x^T\Sigma x$$ $$\hspace{15mm}\text{Subject to}\;\; p^Tx = \frac{1}{n}p^T\boldsymbol{1}$$ ...
0
votes
0answers
37 views

Python: Boundary constraint issue with Scipy.optimize

It seems that I have an issue with my boundary conditions when I use the function [fmin_l_bfgs_b][1]. ...
0
votes
0answers
22 views

Stochastic optimization with unknown distribution function

I have a stochastic optimization problem in which I have expectations both in constraints and objective function and they are both non-linear. Also we do not have any any information about ...
1
vote
0answers
48 views

Thin plate stiffness: analytical formula to validate FEM model

I tried to compute analitically the stiffness of a cantilever thin plate (shown in picture). The plate is also homogeneous and isotropic. The aim is to compare the result I obtain with the result I ...

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