-1
votes
0answers
23 views

Quadratic programming, state of art

I used Gurobi with a MIQP with 26 binary variables and 26*4 interaction term without any other constraint. The speed is very slow already.... I want to ask what is the state of art of MIQP solvers. ...
1
vote
0answers
12 views

Mixed DG for Poisson with mixed BC's

I am trying to find a good reference on a proper weak formulation for mixed DG (Raviart Thomas and DG) formulation for a Poisson equation with mixed boundary conditions. Can anyone suggest a good ...
0
votes
1answer
22 views

2nd Order finite difference for 1D wave equation matlab issue

I'm trying verify that a 2nd order finite difference in space and time approximation of the 1D wave equation is really 2nd order. My Matlab implementation tells me otherwise - I'm not sure of what ...
1
vote
1answer
19 views

Transparent boundary conditions for finite element simulation of TDSE

I have implemented a version of Visscher's method for numerically solving the TDSE (A fast explicit algorithm for the time-dependent Schrödinger equation) (also described in Are there simple ways to ...
0
votes
0answers
20 views

Convected 2nd order tensor in component form [migrated]

I have a convected second order tensor that I'd like to write in component form. $\frac{D\mathbf{a}}{D t} = \frac{\partial \mathbf{a}}{\partial t} + \mathbf{v}\cdot\nabla\mathbf{a}$, where ...
2
votes
1answer
41 views

Solving a pair of high-degree polynomials in two variables with Maple

I have two algebraic equations I am trying to solve in Maple. They are: $14\,{a}^{26}{b}^{2}-91\,{a}^{24}{b}^{4}-364\,{a}^{22}{b}^{6}-1001\,{a} ...
1
vote
1answer
27 views

Is Langevin thermostat/equation correct when trying to model time-dependent behaviour of a molecule?

I've been taught that when simulating a biomolecule in thermal equilibrium, it's best to use the Langevin thermostat - an algorithm which produces a trajectory, which is a realization of a stochastic ...
1
vote
2answers
84 views

How to represent weighted nuclear norm of matrix variable X and minimize it by CVX function, or solve it by other possible packages

I want to minimize $f(x) = \mathrm{Tr}(\sqrt{\mathbf{X}^{T}\mathbf{X}}\mathbf{A})$, where $\mathbf{X}$ is an matrix variable of dimension $d \times d$, and $\mathbf{A}$ is a known matrix. I tried the ...
3
votes
1answer
30 views

How does constraint resolution affect the stability/accuracy of numerical integration?

I understand some basic analysis techniques (local truncation error, global error, zero-stable, absolute stable, etc.) of numerical integration. But I find it hard to apply these techniques in ...
2
votes
0answers
42 views

Euler Equation Eigensystem with Gravity in the Energy Flux

I am modifying a conservative form of the Euler equations with gravity in the energy flux (see previous question: Energy Conservation in Conservation Laws with Source Terms) for use in a Riemann ...
5
votes
1answer
110 views

Numerical evaluation of an elliptic integral in python

Goal: I need to evaluate numerically an integral of the following form: $$ \int_0^\infty \frac{dx}{(a^2+x)\sqrt{(a^2+x)(b^2+x)(c^2+x)}} $$ where $a,b,c \in \mathbb{R}$ are in the interval ...
2
votes
0answers
39 views

Maximize sum of Rayleigh quotients

I want to maximize the sum of Rayleigh quotients: $$\max_x\sum_{i=1}^n\frac{x^\top A_i x}{x^\top B_i x}$$ where $A_i$ and $B_i$ is positive definite. I've found a similar question here: minimization ...
0
votes
0answers
17 views

LBM for thermal anlysis

Can Lattice-Boltzmann methods be used for thermal analysis of radiation or conduction? (Hints for papers and libraries are highly appreciated.)
0
votes
1answer
40 views

Harmonic solution proxies

Does someone know a method to get cheap approximation of harmonic problems (and possibly local approximations)? Let me explain: I need to compute the solution of an harmonic problem \begin{equation} ...
0
votes
0answers
28 views

State of the art in pseudo-boolean optimization

Pseudo-boolean optimization is known to be NP-hard. What is the current state of the art (how many variables, interaction parameters) in solvers for pseudo-boolean optimization problems? What is the ...
0
votes
0answers
12 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
70 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
29 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
27 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
35 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 ...
2
votes
0answers
42 views

Solvers for stiff initial value ODEs with sparse Jacobian

What ODE solvers are optimized for solving stiff systems with sparse Jacobian? Such systems appear, for instance, when a parabolic PDE is discretized in space using typical finite difference or finite ...
1
vote
1answer
81 views

How can I solve this nonlinear, variable-coefficient hyperbolic PDE in one space dimension?

I need to solve the following hyperbolic equation in x and phi co-ordinates $$\frac{\partial \left ( -s/f \right )}{\partial \varphi }+\frac{\partial \left ( 1/f \right )}{\partial x}=0$$ $$\varphi ...
4
votes
2answers
143 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
55 views

The definition of asymptotic convergence?

What is the difference between convergence and asymptotic convergence? Why say the convergence is asymptotic?
0
votes
1answer
38 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
26 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
40 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 ...
-2
votes
0answers
33 views

Can we take transport equation of imaginary quantity? [on hold]

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
40 views

Newton raphson method for finding square root of number [closed]

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
2answers
110 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
99 views

How to set up a shock tube problem such that the solution includes a shock with a specified Mach number

One of the famous and convenient test cases for shock wave modeling is the 1D Sod's shock tube. This is a Riemann problem for the compressible Euler equations of gas dynamics. The initial set up has ...
2
votes
1answer
113 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 $\phi\in[0,1]$, $\theta$, is a random variable ...
0
votes
0answers
36 views

Newcomer of FEniCS, some wrong [closed]

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
120 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 [closed]

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
31 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
43 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 ...
4
votes
1answer
51 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
102 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
166 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
41 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
54 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
33 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
75 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
32 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 ...
1
vote
1answer
79 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
95 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 ...

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