The tag has no usage guidance.

learn more… | top users | synonyms

0
votes
0answers
39 views

Which optimization toolbox is suitable for this type of problem

I have a mixed integer (quadratic/linear) optimization problem with about 3000 variables in a form which I can't extract the coefficient vectores. However MILP solver in Matlab requires the f input ...
0
votes
0answers
60 views

Solving quasilinear/nonlinear equations obtained from the discretization of partial differential equations

When you solve numerically a (system of) linear partial differential equation (PDE) as for example Lapace's equation $\nabla^2\varphi = 0$ or Poisson's equation $\nabla^2\varphi = f$ you obtain a ...
2
votes
0answers
24 views

Disjunctive programming software

Can you advise me any kind of existing software that can help to solve the disjunctive programming problem? The problem is the following. We have unit 3D planes $\Pi_{1}, \ldots, \Pi_{N}$ (they are ...
2
votes
2answers
139 views

Solve non-linear set of three equations using scipy

I need to solve a non-linear set of three equations using scipy. However, I do not have any clue on which algorithm is suitable for my problem from a mathematical point of view (stability, ...
1
vote
0answers
82 views

General algorithm to solve systems of symbolic equations

I want to simplify (solve) a system of linear + nonlinear symbolic equations as much as possible. the equations are of random orders, without differentiation. is there a general & well-known ...
3
votes
1answer
103 views

What is the case of trade-off in different Runge Kutta methods

There are so many Runge Kutta methods, including Dormand-Prince 45 Cash-Karp 54 Fehlberge 78 Is there any comparison between them? What is each approach sacrificing? What is the general ...
2
votes
1answer
85 views

Sparse iterative out-of-core parallel solver

Is there an iterative sparse parallel solver with out of core capabilities? I need to solve a very large system of equations. I have implemented direct sparse parallel solvers in core and out of core ...
1
vote
1answer
87 views

OpenMP threaded nonlinear solver for complex numbers

Problem: I have translated Jacobian-Free Newton-Krylov solver written by C. T. Kelley to Fortran and now want to parallelize it on shared-memory system with OpenMP. In addition, I want to precondition ...
1
vote
1answer
117 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?
2
votes
0answers
67 views

How to tell if symplectic integrator is more suitable for my problem, and what are downsides?

This question follows another one that I have already asked. My intention was to use a classical Runge-Kutta 45 method to solve ODEs of my system. However, I have seen recommendations for using ...
0
votes
0answers
7 views

Is there an existing library that calculates all modes in a step index fiber? [duplicate]

Before embarking on this task I thought it wise to ask if anyone knows of an existing library that does this. I would be coding it in python and at least for starters work on the assumption that ...
6
votes
3answers
160 views

How to write integration tests for numeric simulation software?

Just to be more precise i'll put a worthy example of my typical use case. Let's say I'm developing a FEM software that produces several temporal solutions and inserts them in an HDF5 file, along with ...
2
votes
0answers
233 views

What is numerical damping in the context of time-dependent FEM solvers?

Comsol Multiphysics (a popular FEM package) includes two time-stepping algorithms (IDA aka BDF, and Generalized-alpha), described in their documentation as follows (quoted here under Fair Use; ...
0
votes
2answers
54 views

What is 'SOLVER' in R and Statistics/Analytics ?

**strong text**a) I tried to research on what exactly is a SOLVER only to find a not clear-cut simple answer. My doubts still remain after going through several sites full of discussions about it. I ...
4
votes
2answers
306 views

Solving Lx = b for big sparse Laplacian matrices

What algorithm is more practically suited in terms of performance for solving the $\mathbf{Lx=b}$ equation, where $\mathbf{L}$ is a generic Laplacian matrix (associated to a strongly connected graph, ...
2
votes
2answers
99 views

Suggestions for open source C++ library for medium scale non-linear solver

I need to find the root of a nonlinear system (which comes out of collocation, so I will change the order to test). I will likely have about 50-300 variables, and the Jacobian is going to be ...
4
votes
1answer
131 views

Fast way to repeatedly solve a small nonlinear equation system

A small nonlinear equation system (sizes around 12 ✕ 12) needs to be solved repeatedly (millions of times); each time with some variation in parameters/coefficients (although the equation set is ...
1
vote
2answers
248 views

What sparse linear programming solver it is better to use?

I have the following LP problem: $$ \min \limits_{\varepsilon, x_{1}, \ldots, x_{n}}f(\varepsilon, x_{1}, \ldots, x_{n}) = \varepsilon \;\;\;\;\; s.t. \;\;C x \geq 0, \;\; x_{i}^{0} - \varepsilon ...
4
votes
1answer
280 views

Solver suggestion for many small quadratic problem in C++

I have a C++ program/model that in some parts already use IPOPT (with ADOL-C and ColPack) to solve some pretty large non linear problems. Now in an other part of the program I need to solve a large ...
1
vote
2answers
161 views

Determine the step size in a differential equation numerical solver

How can we define the precision we require in a numerical differential equation solver? What is it that I have to optimize to know? And how do I know that I'm at a sufficient time-step value? For ...
7
votes
2answers
136 views

How do you numerically solve a multivariable ODE system with different time steps per state variable?

If you have a large multivariable ODE system, and certain processes occur at a much smaller time scale, how can you implement a solver that uses smaller time steps for state variables involved in fast ...
3
votes
3answers
142 views

Best method to find the zero of a decreasing function numerically

I need to find the zero of a function $f(\lambda)$ which is of the form $\sum \frac{c_i^2}{(1+\lambda d_i)^2} -1 $. I tried using Newton's method, and it works sometimes, but it is higly dependent of ...
0
votes
0answers
78 views

A question on CHOLMOD

When I change "cholmod_*" to "cholmod_l_" (because the size of my matrix is large, use "cholmod_" will outputs error"problem too large"), it shows " sparse:error: integer and real must match the ...
0
votes
4answers
575 views

Simple FEniCS problem shape mismatch

EDIT: THE ORIGINAL POST DID NOT MAKE MUCH SENSE, SO I ADJUSTED IT Ok, so I have thought about it, googled it and put some more thought into it. This presentation by the Imperial College in London has ...
3
votes
2answers
281 views

Quadratic Programming: Quadprog

Given a real-rectangular matrix $S$ and inorder to solve this simple quadratic programming problem: Minimize $w'S'Sw = ||S w||^2$ over $w$ subject to $e^Tw = 1$ and $w \geq 0$ using a solver I ...
4
votes
1answer
235 views

Solving Coupled ODE eigenvalue problem

I've been trying to find some resources that would help me figure out how to numerically solve a coupled system of ODEs which is also an eigenvalue problem. The system is something like: $ \tag{1} ...
5
votes
1answer
270 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 ...
4
votes
3answers
870 views

CPU benchmarks for numerical kernels

CPU benchmarks available online mostly focus on desktop apps/games and rarely on serial/parallel numerical kernels, specially sparse ones (e.g., MatMult). Some benchmarks like NAS/SciMark exists but ...