Most Popular
1500 questions
10
votes
3 answers
What is the difference between implicit FEM and explicit FEM?
What is the difference between explicit FEM and implicit FEM exactly? According to the post here, it seems that the only difference is whether implicit or explicit time integration is used.
As I remember from one book that I read, implicit FEM is…
Fei Zhu
- 335
- 3
- 9
10
votes
2 answers
Do RBF kernel matrices tend to be ill-conditioned?
I use RBF kernel function to implement one kernel based machine learning algorithm(KLPP),
the resulting kernel matrix $K$ $$K(i,j)= \exp\left({\frac{-(x_{i}-x_{j})^2}{ \sigma_{m}^2}}\right)$$
is shown to be extremely ill-conditioned.The condition…
ZeyuHu
- 317
- 2
- 7
10
votes
2 answers
An Octree Code in Fortran
I am new to scientific computing. I am looking for a Fortran ( preferably f90) implementation of an Octree.
My problem requires an Octree which divides my domain until there aren't more than some N particles(or sources where I know the density value…
rivendell
- 365
- 1
- 9
10
votes
1 answer
Why is it difficult to numerically solve multi-electron time-dependent Schrödinger's equation
It seems that people usually use the Single Active Electron (SAE) approximation to deal with a multi-electron system, transforming the problem into a single electron problem. For example, in numerically solving the problem of a helium atom interact…
xslittlegrass
- 345
- 1
- 2
- 8
10
votes
1 answer
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 system of equations in x,y,z directions which is…
Khine
- 101
- 2
10
votes
2 answers
Is the maximum/minimum principle of the heat equation maintained by the Crank-Nicolson discretization?
I'm using the Crank-Nicolson finite difference scheme to solve a 1D heat equation. I'm wondering if the maximum/minimum principle of the heat equation (i.e. that the maximum/minimum occurs at the initial condition or on the boundaries) also holds…
foobarbaz
- 105
- 5
10
votes
3 answers
How to use polylogarithm function in c++?
Is there any preprocessor directives that could be used to use the polylog function? Or is it included in cmath? If so, do you call it by Li or by polylog?
EDIT:
What I really am trying to do is give an analytical value for the indefinite integral…
flamingohats
- 309
- 4
- 8
10
votes
3 answers
manufactured solutions for incompressible Navier-Stokes -- how to find divergence-free velocity fields?
In the method of manufactured solutions (MMS) one postulates an exact solution, substitutes it in the equations and calculates the corresponding source term. The solution is then used for code verification.
For incompressible Navier-Stokes…
chris
- 1,055
- 7
- 12
10
votes
5 answers
Definition of incompressible flow
As all knows incompressible flow doesn't exist in reality, its an assumption introduced to simplify governing equations. We can not apply this assumption straightforward. Generally Mach number(M<0.3 for incompressible flow), density variation(zero…
Shri
- 222
- 2
- 7
10
votes
5 answers
What is the simplest method for solving incompressible Navier-Stokes equations?
By "the simplest" I mean the simplest to learn and implement from scratch. I hope my question can more or less be answered.
vehsakul
- 335
- 2
- 7
10
votes
2 answers
Solving a linear system with matrix arguments
We're all familiar with the many computational methods to solve the standard linear system
$$
Ax=b.
$$However, I'm curious if there are any "standard" computational methods for solving a more general (finite dimensional) linear system of the form…
icurays1
- 423
- 2
- 9
10
votes
1 answer
What is the impact of C++11 move semantics in the context of scientific computing?
C++11 introduces move semantics which can, for example, improve code performance in situations where C++03 would need to perform a copy construction or copy assignment. This article reports that following code experiences a 5x speed up when…
Matija Kecman
- 505
- 3
- 8
10
votes
4 answers
Matlab : Is there a way to programatically safely halt code execution (like FORTRAN's stop)?
Like the title says, I want to be able to stop the code at a specific location and have it halt safely. I cannot find a command to do it like for example in FORTRAN there is the stop command.
Isopycnal Oscillation
- 610
- 1
- 5
- 14
10
votes
1 answer
What is a good stop criterion when using an iterative method to find eigenvalues?
I read this answer, and realized I have been using the difference between sucessive iterates to define a stop criterion for an iterative method of finding eigenvalues/vectors.
What are good stop criteria for iterative methods that converge to…
Dan
- 3,355
- 3
- 21
- 47
10
votes
1 answer
Quadrature rules, methodologies, and references
There is at least one quite comprehensive encyclopaedia of quadrature rules that doesn't seem to have been updated in quite a while and has restricted access. This source refers to several classical and modern sources, and generally is well put…
Peter Brune
- 1,675
- 12
- 20