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1500 questions
8
votes
3 answers
Laplacian eigenmodes on a semi-circular region with finite-difference method
The computation of eigenmodes of a semi-circular membrane reduces to the following eigenvalue problem
$$\nabla^2u=k^2u\;,$$
where the region of interest is a semi-circle defined by $r\in[0,1]$ and $\varphi\in[0,\pi]$.
It is appropriate to work in…
liberias
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- 5
8
votes
2 answers
Filtering a dataset to get a more uniform distribution for neural network training
I'm looking into using artificial neural networks (ANN) to predict the reaction rates in my fluid instead of solving the full system of stiff ODEs. Some people from my lab have already done some work on that so I don't start from scratch but I am…
FrenchKheldar
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- 22
8
votes
2 answers
Shape regularity in higher dimensions
In Finite Element theory, and other methods in scientific computing for PDEs, one uses meshes which fulfill several regularity criteria, many of them being equivalent.
It is of interest to have notions of shape-regularity in arbitrary dimensions.…
shuhalo
- 3,660
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- 31
8
votes
1 answer
Why am I getting so much error for my Runge Kutta Fehlberg solver?
My current project is a reprogramming of a protein folding model involving the solution of thousands of ODEs in C++. I've been making some stop and start progress as I'm writing the solver to run totally on the GPU. I finally got it integrating but…
Hair of Slytherin
- 277
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- 10
8
votes
2 answers
How do you numerically solve a multivariable ODE system with different time steps per state variable?
If you have a large multivariable ODE system, and certain processes occur at a much shorter time scale, how can you implement a solver that uses smaller time steps for state variables involved in fast processes, and large time steps for state…
bmillare
- 181
- 1
8
votes
3 answers
Solving a non-symmetric non-diagonally dominant sparse system the best way
I faintly recall from my early "numerics" lectures that iterative linear solvers for $Ax=b$ often require that when $A$ is decomposed as
$$A=D + M$$
where D is a diagonal matrix and $M$ has zero diagonal,
the elements of $D$ should be dominant…
Lagerbaer
- 487
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8
votes
1 answer
Finding the fixed point of an operator
What numerical methods are available for finding the fixed point of an operator $A$ that is acting on functions $f : [a,b] \rightarrow [a,b]$? I am looking for the function $f$ for which $Af = f$.
Essential details:
My function $f$ is actually a…
Szabolcs
- 2,620
- 2
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8
votes
1 answer
F(x) = 0 vs. ||F(x)||^2->min
In many areas of application, one needs to solve a nonlinear system of equations
$$
F(x) = 0.
$$
Sometimes, the formulation
$$
\|F(x)\|^2 \to\min
$$
is used. Clearly, every solution $\hat{x}$ of $F(x)=0$ is also a solution of the second problem; the…
Nico Schlömer
- 3,126
- 17
- 36
8
votes
1 answer
Automatically generating finite difference matrices for systems of PDEs
Suppose that you have a system of PDEs to solve. At least for simplicity, let's assume it's time independent, quasi-linear (linear in its derivatives) solved on a rectangular grid in (x,y) space, and with boundary conditions specified all around. My…
TSGM
- 303
- 1
- 6
8
votes
2 answers
How to deal with norm inequality constraints
I want to solve the (convex) optimisation task:
$max_{r,z}\quad r$
subject to the following two constraints
$r\|x_i\| - x_i^Tz \leq 0 \qquad \forall i=1,\dots, N $
$\|z\| \leq 1$
$r\geq0$
$r$ is a scalar, $z$ is a vector, the $x_i$'s are vectors of…
dgray
- 113
- 1
- 5
8
votes
2 answers
Minimum path on known potential surface
I'm searching for the minimum path between the minima of a potential surface that is already known on a grid.
(source: http://www.math.nus.edu.sg/~matrw/string/)
Any point on the path is at an potential minimum in all directions perpendicular to…
tmartin
- 209
- 1
- 7
8
votes
1 answer
Generalized Singular Value Decomposition: only compute the r largest singular values
I want to compute the Generalized Singular Value Decomposition for sparse matrices with a size of up to 1000000 x 1000000 (not necessarily square). The method is going to be used in machine learning (classification).
Currently I'm using the function…
Matthias Munz
- 181
- 7
8
votes
1 answer
MPI policy for multiple asynchronous transfers
What is the policy of multiple overlapping asynchronous transfers in MPI?
I have a program with several open asynchronous irecv operations. I find that transfers that could take place (the corresponding isend has been called) wait on other…
MRocklin
- 3,088
- 20
- 29
8
votes
1 answer
Solving a large non-hermitian generalised eigenvalue problem from a linear stability analysis using SLEPc
I have a generalised matrix problem: $A x = \lambda B x$ from a spectral method on a linear stability analysis problem. My matrix B is diagonal and positive semi-definite. A is non-hermitian and complex.
My problem is essentially that when using the…
Toby Searle
- 81
- 2
8
votes
2 answers
How to decide stability of Runge-Kutta method for non-linear ODE?
I'm working on a parameter study of Duffing's equation
$\ddot x + \delta \dot x + \alpha x + \beta x^3 = \gamma \cos{\omega t},$
where $\delta, \alpha, \beta, \gamma$ and $\omega$ are real parameters and $\dot x := dx/dt$. Substituting $x…
trolle3000
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