Unanswered Questions

19
votes
0answers
410 views

Difficulty with Spectral Method using Chebyshev Polynomials

I am having a bit of difficulty in trying to understand a paper. The paper uses spectral method to solve for an eigenvalue that comes from a system of coupled ODEs. I will write out only one equation ...
14
votes
1answer
513 views

Are there any open source inverse-based multilevel ILU implementations?

I am very impressed with the serial performance of multilevel inverse-based ILU preconditioners, particularly for heterogeneous Helmholtz, but I am surprised to not be able to find any open source ...
11
votes
1answer
748 views

Dirichlet-Neumann boundary condition solution becomes unstable - Pressure Correction Method

I am simulating incompressible flow over a cylinder at Reynold number of 500. I am solving navier stokes equation using pressure correction method. My solution becomes unstable after certain time ...
10
votes
0answers
379 views

Diagonal update of a symmetric positive definite matrix

$A$ is a $n \times n$ symmetric positive definite (SPD) sparse matrix. $G$ is a sparse diagonal matrix. $n$ is large ($n$ >10000) and the number of nonzeros in the $G$ is usually 100 ~ 1000. $A$ has ...
9
votes
0answers
94 views

Why are Octrees used for Multipole space decomposition?

In most (all?) implementations of the Fast Multipole Method (FMM), octrees are used to decompose the relevant domain. Theoretically, octrees provide a simple volumetric bound, which is useful for ...
9
votes
1answer
675 views

Boundary conditions in fluid simulation

I'm working on a 2D fluid sim using vortex particles/"vortons" as described in Fluid Simulation for Video Games. Which I think is the same things as the "discrete vortex method". Basically you ...
9
votes
0answers
128 views

Specialized methods for symmetric tridiagonal generalized eigenvalue problems

I have to solve generalized eigenvalue problems $Ax = \lambda Bx$ where $A$ and $B$ are both tridiagonal, $B$ is symmetric positive definite and real, but $A$ is only complex symmetric (not definite ...
8
votes
0answers
193 views

Implementation of Jacobi-Davidson method for cubic eigenvalue problem

I have a large cubic eigenvalue problem: $$\left(\mathbf{A}_0 + \lambda\mathbf{A}_1 + \lambda^2\mathbf{A}_2 + \lambda^3\mathbf{A}_3\right)\mathbf{x} = 0.$$ I could solve this by converting to a ...
8
votes
0answers
482 views

Comparing Jacobi and Gauss-Seidel methods for nonlinear iterations

It is well known that for certain linear systems Jacobi and Gauss-Seidel iterative methods have the same convergence behavior, e.g. Stein-Rosenberg Theorem. I am wondering if similar results exist for ...
7
votes
0answers
160 views

Operator Splitting methods for non-standard forms

After doing some research, I've found that most of the literature on operator splitting methods (e.g. Strang Splitting, Fractional Step, etc.) are specifically designed for a standard problem type of ...
7
votes
0answers
276 views

Simple turbulence model appropriate for buoyancy-driven cavity like problem

Which turbulence model is suitable for resolving incompressible buoyancy-driven flow of a fluid within an cylindrical ampoule? I prefer turbulence model which is sufficiently simple so that fully ...
7
votes
0answers
211 views

cuda and numerical methods with implicit time discretization

I am looking to port some code that resolves a set of partial differential equations (PDE) by the finite volume method in IMPLICIT form (for the time discretization). As result there is a tridiagonal ...
7
votes
0answers
137 views

How does positivity preservation fit into the implication chain from monotone to monotonicity preserving?

I know from "Numerical Methods for Conservation Laws" by Randall J. LeVeque that there is an implication chain of properties of methods for conservation laws: monotone $\Rightarrow$ $L^1$-contractive ...
7
votes
0answers
262 views

What's a good numerical/optimization software package for solving the 2-D optimal stopping problem?

I am looking for a numerical software package to help me solve the 2-dimensional "free boundary" PDEs that arise in optimal stopping problems. In one dimension a standard optimal stopping problem in ...
7
votes
1answer
149 views

Bounding the relative error of derivative given relative error of the function

Suppose a function $f$ can be computed such that the bound on the relative error is $R$ i.e. $f^-(x) = f(x)(1+r)$ where $f^-$ and $f$ are respectively the computed and exact value $f$ and $|r| \leq ...

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