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Top new questions this week:

solving linear system whose symmetrized matrix is positive definite

Are there iterative methods for the solution of nonsymmetric linear systems $Ax=b$ that can take (theoretical or practical) advantage from knowing that $A+A^T$ is positive definite? These matrices are ...

linear-solver iterative-method  
asked by Arnold Neumaier 6 votes

How does the number of function calls in BFGS scale with the dimensionality of space

Is there any estimate for the scaling of the number of function calls in BFGS-optimization with the dimensionality of the search space? Specifically I am assuming a (free) expression for the gradient ...

optimization scaling  
asked by Kvothe 4 votes
answered by Infinity77 6 votes

Check if LinearOperator is symmetric

I have a scipy.sparse.linalg.LinearOperator object. I'd like to check if its associated matrix is symmetric without actually instantiating the matrix in the most ...

linear-algebra scipy  
asked by Alex L 3 votes

How does the error work for the Strang Splitting?

We know in Strang splitting that the splitting error in the steady state solution is proportional to $h^2$. I want ask 2 things: If this error in the steady state solution is the global error? If we ...

nonlinear-equations operator-splitting  
asked by Giannis Kavroulakis 2 votes

Why is bounding a surface with a capsule is better than with a cylinder to detect intersections?

In this article: https://www.geometrictools.com/Documentation/IntersectionOfCylinders.pdf the writer says: "If you plan on using cylinders for bounding volumes in a real-time graphics engine—...

computational-geometry  
asked by Eminem 2 votes

A priori error estimates - finite element method - mixed boundary conditions

Consider the problem $$ \left\{\begin{array} {rcl} -\Delta u & = 0 & \text{ in } \Omega \\ u & = 0 & \text{ on } \Gamma_D \\ \frac{\partial u}{\partial n} &= g &\text{ on } \...

finite-element reference-request  
asked by Beni Bogosel 2 votes

Manufactured solution for $-\operatorname{div}(a(x) \nabla{u}) = f$ when $\alpha(x)$ is discontinuous

I'm studying the dealii tutorial number 4,5 and I understand the workflow. I've also been able to find the EOC by using manufactured solution where $f$ is a smooth r.h.s. and $\alpha(x)$ smooth too. ...

finite-element convergence poisson deal.ii weak-solution  
asked by bobinthebox 1 vote
answered by cfdlab 1 vote

Greatest hits from previous weeks:

2D Ising Model in Python

I am trying to calculate the energy, magnetization and specific heat of a two dimensional lattice using the metropolis monte carlo algorithm. ...

python computational-physics monte-carlo  
asked by P.Blah 2 votes
answered by Christophe 3 votes

How does the MATLAB backslash operator solve $Ax=b$ for square matrices?

I was comparing a few of my codes to "stock" MATLAB codes. I am surprised at the results. I ran a sample code (Sparse Matrix) ...

linear-algebra performance matlab  
asked by Inquest 38 votes
answered by Allan P. Engsig-Karup 40 votes

Constraints involving $\max$ in a linear program?

Suppose $$\begin{align*} \min A &\mathrm{vec}(U) \\ &\text{subject to } U_{i,j} \leq \max\{U_{i,k}, U_{k,j}\}, \quad i,j,k = 1, \ldots, n \end{align*}$$ where $U$ is a symmetric $n\times ...

optimization linear-programming  
asked by N21 16 votes
answered by Geoff Oxberry 14 votes

Why is my iterative linear solver not converging?

What can go wrong when using preconditoned Krylov methods from KSP (PETSc's linear solver package) to solve a sparse linear system such as those obtained by discretizing and linearizing partial ...

linear-algebra petsc preconditioning krylov-method iterative-method  
asked by Jed Brown 27 votes

How do I calculate the numerical difference between two fields stored in two different VTK files with the same structure?

Suppose I have two VTK files, both in structured grid format. The structured grids are the same (they have the same list of points, in the same order), and there is a field, call it "Phi", in each VTK ...

visualization vtk  
asked by Geoff Oxberry 15 votes
answered by Geoff Oxberry 16 votes

Importance of the Time Step Value for the Accuracy of a Transient CFD Simulation

Overview My understanding is that one should use a time step $\Delta t < \frac{h}{v}$ (where h - smallest mesh element, v - velocity) to get an accurate result. But how important is this really ...

fluid-dynamics  
asked by A.L. Verminburger 8 votes
answered by Wolfgang Bangerth 12 votes

How to determine the amount of FLOPs my computer is capable of

I would like to determine the theoretical number of FLOPs (Floating Point Operations) that my computer can do. Can someone please help me with this. (I would like to compare my computer to some ...

floating-point  
asked by Ol' Reliable 21 votes
answered by Max Hutchinson 13 votes

Can you answer this question?

Stability plot of upward difference implicit time

I am analyzing the stability of 1D convection (advection) equation as shown in the picture. When I derive the equations as shown I want to get rid of the complex number. I`m asking if those stability ...

pde finite-difference stability advection  
asked by Abdelrahman Mabrouk 1 vote
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