Unanswered Questions

15
votes
1answer
751 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
0answers
174 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 ...
10
votes
1answer
175 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 ...
10
votes
1answer
422 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 ...
9
votes
0answers
928 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 ...
8
votes
0answers
139 views

scale invariance for line-search and trust region algorithms

In Nocedal & Wright's book on Numerical Optimization, there is a statement in section 2.2 (page 27), "Generally speaking, it is easier to preserve scale invariance for line search algorithms than ...
8
votes
0answers
80 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
207 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
103 views

Time advance in Adaptive Mesh Refinement method

I am working on solving complex system of 2D PDEs governing the behaviour of plasma in a gas lamp during discharge. Recent tests have shown that because of steep gradients in temperature field and ...
7
votes
0answers
64 views

Are there any standardized file formats for point group character tables?

Character tables are an important tool for symmetry analysis in many computational chemistry software packages. Are there any standardized file formats for point group character tables? This may seem ...
7
votes
0answers
325 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
370 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
314 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
127 views

Verification in Eigenvalue problems

Let us start with a problem of the form $$(\mathcal{L} + k^2) u=0$$ with a set of given boundary conditions (Dirichlet, Neumann, Robin, Periodic, Bloch-Periodic). This corresponds with finding the ...
6
votes
0answers
140 views

Is there a faster method to compute the geometric series of a matrix?

I want to calculate the geometric series of a matrix $A$: $$S=I+A+A^2+\dots+A^n$$ and then apply to a vector $v$, $Sv$. I've done it in Matlab with a loop and I think it's quite efficient applying ...

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