Unanswered Questions

19
votes
0answers
427 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 ...
15
votes
1answer
577 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
0answers
438 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
119 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
0answers
135 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
36 views

Evaluating oscillatory integrals with many independent periods and no closed forms

Most methods for oscillatory integrals I know about deal with integrals of the form $$ \int f(x)e^{i\omega x}\,dx $$ where $\omega$ is large. If I have an integral of the form $$ \int ...
8
votes
1answer
83 views

Method to quantify geometric difference of two dissimilar meshes

I am looking for a method or algorithm to produce a value that describes how different two meshes are geometrically but that have different topologies. An example would be some CAD data that has had ...
8
votes
0answers
218 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
644 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
169 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
287 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
252 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
141 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
280 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 ...
6
votes
0answers
123 views

Sequential approach to solving coupled PDEs

I'm dealing with a coupled system of three transient, non-linear convection-diffusion equations. Let's just say to simplify the problem that they take the following form: $$ ...

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