Unanswered Questions

5
votes
0answers
49 views

Standard format for character tables of point group symmetry

Symmetry is a very useful abstraction that can be used in various scientific area. Group theory provide a solid ground on which many well established and efficient methods have been developed. For ...
1
vote
0answers
21 views

fixed point iteration to find out second order non-linear diff equations

I am working on some model analysis, getting two diff equations and after I convert them into matrix form, I have equations looks like $$ [A][X]=C\times\big(\exp([B][X])-1\big), $$ where $C$ is a ...
1
vote
0answers
79 views

Differences in answers between Python and Fortran

I am translating a piece of Fortran code into Python and am testing my code with a certain test case. All the results differ with 0.04% compared to the Fortran results. This is a very small ...
1
vote
0answers
74 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 ...
15
votes
1answer
695 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 ...
10
votes
1answer
393 views

Danger of complex arithmetics in scientific computing

The complex inner product $\langle u,v\rangle$ has two different definitions decided by conventions: $\bar{u}^Tv$ or $u^T\bar{v}$. In BLAS, I found the routines cdotu, zdotu, and cdotc, zdotc. The ...
10
votes
0answers
169 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
897 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 ...
9
votes
0answers
150 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
78 views

Guidelines for nested preconditioners

Consider the situation where you want to solve a linear system using a preconditioned Krylov method, but applying the preconditioner itself involves solving an auxiliary system, which is done with ...
8
votes
0answers
200 views

Operator Splitting methods for DAEs

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
324 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
351 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
313 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
56 views

energy drift in molecular dynamics

I hope the following question will not be perceived as to vague. I am trying to ask the question directly, without going into too much information regarding my code. I am currently developing a ...

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