Questions tagged [solver]

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Examples of problems that cannot be formulated as optimization problems

An optimization problem has 3 main components: decision variables, constraints and an objective function. Such a problem can be mathematically modelled and solved using an optimization solver. For ...
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Non linear Parametric BVP with inequalities

Consider a non linear ode in dimension $10$: $\dot x = f(t,x,\lambda)$ where $\lambda$ is a vector of $p$ parameters. Consider a boundary value problem of the form : $\dot x(t) = f(t,x(t),\lambda)$ ...
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Discrete-time Algebraic Riccati Equation (DARE) solver in C++

I need to use a Discrete-time Algebraic Riccati Equation (DARE) solver for an embedded controller (with limited processing power) in a research project and sadly, I can't find any implementation of it ...
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What is the difference between Abaqus and Calculix contact input?

I would like to say first that am new at using Calculix. I'm using Abaqus/CAE to create a cup deep drawing simulation and everything worked perfectly but my objective is to run the same exact ...
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How can a CG solver solve a non positive definite sparse matrix

I am using the CUSP CG solver and I ran it on couple of sparse matrices from the University of Florida sparse matrix collection. The solver was able to solve non positive definite sparse matrices. My ...
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How to model a non-linear least-squares problem for triangles

I have a non-linear least-squares problem to solve and with my current modeling the solver is either very slow or does not converge to a correct solution. For the problem I need to minimize an energy ...
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How to measure efficiency of the differential equations solver

I want to compare a few solvers of partial differential equations. I need to include the computational time and the solution accuracy (compared to analytical solution or something similar). What kind ...
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Are there generic formulations of Riemann solvers?

I have been following Toro's book on Riemann solvers to implement a finite-volume scheme for computational fluid dynamics. The Riemann solvers presented in the book seem to be fairly tightly coupled ...
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I am trying to solve a system of non-linear index-1 DAEs in which the derivatives of the state variables, $x(t)$ are corrupted by additive noise, $w(t)$ (whose co-variance matrix is known). $\dot x(t)... 0answers 74 views Three steps of pde numerical solution and nonlinear equation I'm very new here. I'm trying to solve nonlinear elliptic equation $$(n(u)u')' = f(u)$$ and face with crucial misunderstanding. As I suppose, the procedure of solving some nonlinear equation ... 1answer 267 views Comparison between CashKarp Method and Dormand Prince Method - Runge Kutta Method Can Cash Karp Method be used for integrating a nonsmooth solution ?. Because Dormand Prince method gives an error while integrating nonsmooth solution How can nonsmooth function can be integrated? I ... 2answers 331 views Direct Solver and domain decomposition In finite element method, in order to use MPI, we need to decompose the domain into sub-domains first. Then my question is whether we can solve each sub-domain using a direct solver? Of course, unlike ... 1answer 41 views Express the$\gamma_{2}^{\epsilon}$SemiDefinite program in a form that is acceptable by SDPT3 I'm trying to express the following semidefinite program: for given$A \in R^{m \times n}$and a scalar$\epsilon \in (0,1), \begin{align} &\gamma_{2}^{\epsilon}(A):= \min\,t\\ &\text{... 1answer 326 views Best platform for complex SDPs with n and m around 5-15K? I am looking to solve a class of SDPs with complex entries, with the semi-definite coneS^n$,$n$around 5000 to 15000. Also,$m$, the number of equality/inequality constraints is close to$n$. I ... 2answers 536 views abaqus solver question I want to solve a pair of ODEs using the FEM solver of Abaqus. Is it possible for the user to supply the equation and ask Abaqus solver to solve the equations? 1answer 216 views Solve a pair of coupled nonlinear equations within certain limits This answer to this question works only for situations in which the desired solution to the coupled functions is not restricted to a certain range. But what if, for example, we wanted a solution such ... 0answers 54 views Which optimization toolbox is suitable for this type of problem [duplicate] 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 ... 0answers 87 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 ... 2answers 4k 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, ... 0answers 459 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 ... 1answer 549 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 trade-off ... 1answer 147 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 ... 1answer 214 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 ... 1answer 261 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? 0answers 89 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 ... 3answers 273 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 ... 1answer 3k 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; ... 2answers 798 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 ... 2answers 1k 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, ... 2answers 235 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 ... 1answer 244 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 ... 2answers 1k 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 \... 1answer 930 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 ... 2answers 1k 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 ... 2answers 158 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 ... 3answers 617 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 $. I tried using Newton's method, and it works sometimes, but it is higly dependent of ... 1answer 211 views A question on CHOLMOD: long int vs int, still failing after change to long int [closed] Changing cholmod_* to cholmod_l_* results in the following error: sparse:error: integer and real must match the routines ... 4answers 1k views Simple FEniCS problem shape mismatch EDIT: THE ORIGINAL POST DID NOT MAKE MUCH SENSE, SO I ADJUSTED IT Ok, so I have thought about it, googled it and put some more thought into it. This presentation by the Imperial College in London has ... 2answers 429 views Quadratic Programming: Quadprog Given a real-rectangular matrix$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$using a solver I ... 1answer 495 views Solving Coupled ODE eigenvalue problem I've been trying to find some resources that would help me figure out how to numerically solve a coupled system of ODEs which is also an eigenvalue problem. The system is something like:$ \tag{1} ...
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 ...