0
votes
0answers
5 views

Max weighted subset (max sum diversification)

Given a set of elements $V$, with known cost $\pi_S$ for each subset $S \subset V$ and a monotone increasing function on the subsets $f(S)$ . I'm wondering if there is a pseudo-polynomial algorithm ...
0
votes
1answer
21 views

Domain Decomposition with PETSc

Does anyone have any experience on Domain Decomposition using PETSc library? I have used PETSc for creating my vectors and matrix within my C++ code. I also used KSP to solve the linear system. I ...
0
votes
1answer
21 views

Implicitly defined univariate function

So my fellow numerical computational peeps it may be that I am suffering from sleep deprivation but I'm struggling to numerically compute a function $u \rightarrow h(u)$ defined implicitly as follows: ...
0
votes
0answers
19 views

Solving a nonlinear equation with a Markov process and RVs

Assume that we have the following equation and the following assumption. The scope is to solve for some particular variables expressed later. Update $$E_{t}\left[ b(A_{t+1})^{1-\gamma} ...
0
votes
0answers
23 views

Solvers for nonlinear parabolic PDEs

Could you please advise some programs or libraries for solving parabolic PDEs (or its systems) in 1D, 2D and 3D, for example, with the method of lines? The system of parabolic PDEs can be nonlinear in ...
0
votes
0answers
22 views

Sparse ODE solvers

What ODE solvers are optimized for solving sparse ODE systems? Such systems appear when the method of lines is used for solving parabolic PDEs.
0
votes
0answers
18 views

modify a Riemann solver in clawpack to solve a hyperbolic pde

I need to solve a hyperbolic equation in clawpack (or if you can help me to find another hyperbolic pde package) but I dont know How to modify a standard Riemann solver or write a solver for specific ...
3
votes
1answer
87 views

Crank-Nicolson method for solving nonlinear parabolic PDEs

Is the Crank-Nicolson method appropriate for solving a system of nonlinear parabolic PDEs like $\partial u/\partial t - a\Delta u + u^4 = 0$ ? I tried to apply this method for solving such system but ...
1
vote
1answer
38 views

The definition of asymptotic convergence?

What is the difference between convergence and asymptotic convergence? Why say the convergence is asymptotic?
0
votes
1answer
21 views

number of control points for B spline curve

I am trying to use B spline curve fitting. The order of B spline curve is 4. When I have many control points, it works well. However if the number of control points is small such as two, my program ...
2
votes
1answer
18 views

Combinatorial optimization problem: choose a set of corrective factors to make a set of points most closely resemble a plane

Apologies in advance if this has already been asked before (I suspect it has, but I'm not experienced to know what to call it, or how to classify this problem). Given a set of $m$ points in space, ...
-1
votes
1answer
34 views

Libraries with the method of lines for parabolic PDEs [on hold]

Could you please advise some programs or libraries for solving parabolic PDEs (or its systems) in 1D, 2D and 3D, for example, with the method of lines? The system of parabolic PDEs can be nonlinear in ...
6
votes
3answers
1k views

Do they use semidefinite programming in industry?

I can't see any mention of it in job listings. I've seen mentioned integer programming, MIP, mixed-integer nonlinear programming, LP, dynamic programming etc., but no SDP. Is it much trendier in the ...
-1
votes
0answers
27 views

Can we take transport equation of imaginary quantity?

The question is asked in Physics StackExchange and it didn't turn out to be fruitful so I am posting it here. In the RANS equation we approximate the nonlinear fluctuating terms to eddy viscosity ...
-1
votes
0answers
39 views

Newton raphson method for finding square root of number [on hold]

I am trying to use the newton raphson method for finding square roots. Considering the function f(x)= c-x^2 if we solve for f(x) =0 then x = square root of c which is what we want to find ...
2
votes
1answer
94 views

How many generations does it typically take for a differential evolution method to reach a global optimum?

For differential evolution methods in optimization, how many generations does it typically take to reach a global optimum? How do we know if the values are never going to converge?
3
votes
2answers
75 views

How to determine the initial values of compressible Euler equations for shock wave problem by knowing initial Mach number?

One of the famous and convenient test case for shock wave problem is Sod's Shock tube test case for 1D PDEs. The initial set up has been done by dividing domain half with diaphragm. Left and right ...
2
votes
1answer
92 views

Solving a nonlinear equation with random variable

I would like to solve an equation that looks like this UPDATE $E[(R^{1-\gamma})(r_k+\theta-r_z)]=0$ , where $R=\phi r_z+(1-\phi)(r_k+\theta)$ and $\phi\in[0,1]$, Thus $E[(R^{1-\gamma})\theta]=0$ ...
0
votes
0answers
32 views

Newcomer of FEniCS, some wrong [on hold]

everyone, I am a newcomer of FEniCS, Today I just installed the FEniCS tool, Then I have tried a example of implementing the codes about 2D Poisson equations coming from the FEniCS tutorial (see enter ...
4
votes
0answers
104 views

Why does Matlab's integral outperform integrate.quad in Scipy?

I am experiencing some frustration over the way matlab handles numerical integration vs. Scipy. I observe the following differences in my test code below: Matlab's version runs on average 24 times ...
-1
votes
1answer
20 views

Help compiling with GSL [on hold]

I'm looking into using GSL (GNU Scientific Library) for work. I'm primarily needing to use the statistics and linear algebra functionality. I am having a very tough time getting the example code on ...
1
vote
1answer
30 views

Matlab equivalent of scipy's 'vode' and 'zvode' ode routines

In python I have used the ode method from scipy.integrate. There I used the vodeintegrator ...
5
votes
1answer
38 views

How to estimate the local error and the global error for Runge-Kutta method

How to estimate the local error and the global error for Runge-Kutta method used for solve a system of differential equations in practice? I use Richardson extrapolation for select a adaptive step ...
3
votes
1answer
45 views

Where to find CAD and mesh models for tests?

I often find in the literature some numerical tests use CAD and mesh models. I also want to reproduce their results or test my algorithms on those models. But I am not trained to use CAD or mesh ...
0
votes
2answers
91 views

Numerical method of lines for solving PDEs

Could you please advise some literature about the numerical method of lines (MOL) for parabolic PDEs? It is a method of solving PDEs with discretizing only by space but not by time. A system of ODEs ...
3
votes
2answers
158 views

Parallel optimization algorithms for a problem with very expensive objective function

I am optimizing a function of 10-20 variables. The bad news is that each function evaluation is expensive, approx 30 min of serial computation. The good news is that I have a cluster with a few dozen ...
0
votes
2answers
40 views

Matrix size LAPACK can support with level-3 BLAS

I am a newbie in using LAPACK library. I know that LAPACK's internal rountines break the large problem into smaller problems recursively (I am considering level-3 BLAS). If we consider matrix ...
3
votes
1answer
50 views

Apply for a cluster for scientific computing from a developing country?

I don't have access to a computer cluster in my university. Is there website that accepts applications for free access to a computer cluster for scientific computing? Further information: I am in ...
3
votes
1answer
30 views

Numerical Principal Value Integration - Hilbert like

I'ld like to calculate the PV of an integral with the form $$ \tilde{G}_l(\omega) = -\frac{2\omega}{\pi} PV\int_0^\infty \frac{\tilde{G}_d(\omega^\prime)}{\omega^2 - {\omega^\prime}^2}d\omega^\prime$$ ...
2
votes
1answer
70 views

Finite differences scheme for 2D advection equation

I'm trying to study with a finite difference method the 2D advection equation with a space-dependant flow. Taking a function $f(x,y,t)$ solution of the equation : $$ ...
0
votes
0answers
20 views

Cardiac Excitation Threshold in C++ modelling

So I am trying to write a code in C++ about the cardiac excitation threshold. I know that this excitation threshold is the shortest stimulus2 value at which it can conduct an action potential (known ...
1
vote
1answer
40 views

How to calculate collision force with no future knowledge

For a personal project, I am attempting to write a fairly realistic collision simulator (for relatively large objects, not quantum stuff). As I was consulting my physics textbook and various online ...
0
votes
0answers
30 views

total memory usage of MPI shared memory

I am trying to use the MPI share memory feature. I have several SMP nodes, and each of them has four cores. I need an array of size N for each node that should be accessed by all four cores in each ...
0
votes
0answers
21 views

In COMSOL, what is the difference between all the “Studies”? [closed]

When I right-click on (root)->Add Study, I can choose between: Eigenfrequency Frequency Domain Frequency-Domain Modal Mode Analysis What is the difference between all of them? Isn't the ...
1
vote
1answer
78 views

How does the number of iteration until optimization begins depends on the dimension of the problem?

I am optimizing a function of 10-20 variables by running algorithm such as BOBYQA and a few other derivative-free algorithms. The bad news is that each function evaluation is very expensive, approx 30 ...
4
votes
2answers
88 views

Condition number from incomplete Cholesky factorization

I'm having difficulties patching together from what I read about obtaining the condition number of a real, symmetric, positive definite sparse matrix. In my code, I found that there is incomplete ...
1
vote
1answer
135 views

matlab: []*[] == [] makes vectorized code difficult

In my (admittedly brief) experience, there have been instances in which the code got uglier because []*[] == [], and it would be possible to write more elegant code if it was defined to be 0 instead. ...
0
votes
0answers
11 views

Double integrals and parameters in GSL

I'm trying to calculate a numerical integral in C. I have a function that depends on several variables, two of which I want to integrate over while leaving rest of them as parameters. I was going to ...
0
votes
1answer
44 views

Is it possible to output the matrix condition number from pardiso (MKL)? [closed]

I am assuming the pardiso solver calculates (or estimates) the condition number before proceeding to the solution phase. Is there a way to make pardiso output the condition number? Alternatively, ...
13
votes
1answer
123 views

Puzzling remark about stability region of fifth-order Runge-Kutta method

I came across a puzzling remark in the paper P. J. van der Houwen, The development of Runge-Kutta methods for partial differential equations, Appl. Num. Math. 20:261, 1996 On lines 8ff on page 264, ...
2
votes
0answers
29 views

Produce one smooth curve on one triangle mesh

I hope to get one smooth curve on one triangle mesh. I get one path on the mesh at first. The path consists of vertices of the mesh. I can see the path from the image below. Each one green dot ...
3
votes
2answers
37 views

Derivative-free nonlinear optimization of discrete objective function with linear constraints (simplex)

I am trying to optimize a constrained-problem with a discrete, non-linear objective function. Evaluating this function is also fairly expensive. Nevertheless, despite the above two factors, I hope, ...
0
votes
0answers
20 views

computational science fortran 90 solar cycle fortran model [migrated]

I'm a new fortran user. I've been given a task and I'm not quite sure how to tackle it. The task is: **Solar radiation is an energy source which plays a central role for atmospheric processes. Half ...
5
votes
3answers
107 views

Test Case with Known Solution for 3D Navier Stokes Equations

Is there a test case for 3D incompressible Navier Stokes Equations like the Taylor vortex in two dimensions? I know, I can easily construct 3D manufactured solutions but I would like to have ...
4
votes
1answer
52 views

Error implementing Robin boundary conditions in toy ODE problem

I am attempting to solve the following ODE problem: $$-u''+ u = x$$ $$u(0) = 0$$ $$u'(1) = -u(1)$$ The exact solution is: $u(x) = e^{-x-1} - e^{x-1} + x$ I have a Dirichlet at $x = 0$ and a Robin ...
5
votes
1answer
79 views

Solving Generalization of Saddle point problem

I am interested in knowing if there is a generalization of the Uzawa iteration for the linear problems of the form $$\left[ \begin{array}{ccc}A& B^T&0\\ B&0&C^T\\ 0&C&0 ...
1
vote
1answer
70 views

Solving Advection (Convection) - Diffusion - Reaction Partial Differential Equation in Python

I am looking for library written in Python which will enable me to solve the coupled nonlinear equations which looks like: I need the library which will enable me to couple this solver to other ...
1
vote
3answers
78 views

Minimize quadratic form with equality constraints

I want to minimize function: $f(x) = x^T \cdot A \cdot x + b \cdot x$ given constraints: $B \cdot x = 0$. Here: $x$ is a vector ($x \in \mathbb{R}^n$), $A$ is a matrix of size $n \times n$, $b$ ...
2
votes
1answer
75 views

What is the exact formulation of compressible Euler equation of gas dynamics in polar coordinates with artificial diffusion in 2D?

The interested equation is advection-diffusion equation. One of the canonical example is Navier-Stokes equations. However, I would like to let the coefficient of diffusion constant goes to zero, ...
0
votes
0answers
20 views

random permutations by probability matrix [closed]

I have the following problem: I need to generate L random samples of N-position permutations from M>=N elements by predefined probability NxM matrix P. Distribution probability matrix P = {p_I,J} ...

15 30 50 per page