Computational Science Questions, Problems & Solutions : TransWikia.com ~ Page 6

Solving coupled ODEs using Runge-Kutta method

I want to solve the following sets of $n$ coupled equations. Initial values of $x_{n}(t)$ and $p_{n}(t)$ are specified. The problem is, I have an 1D lattice...

Asked on 10/23/2021

3 answer

Writing code on the CPU while developing, running it on the GPU when live - which approach?

In my simulations I am using dense matrix-vector multiplications and 2D-fft transformations quite often, for matrix sizes of 8kx8k and up. Hence, I assume that using a GPU is beneficial...

Asked on 10/23/2021

2 answer

Non-negative least squares with very small numbers

(I have asked this question on StackOverflow previously but it has been pointed to me that CSSE or MSE could be more appropriate) I have to solve a constrained optimization...

Asked on 10/23/2021

1 answer

Matlab - Fast Computation of Truncated SVD / PCA

I'm working with a Matlab codebase wherein I'm attempting to solve A*c = b by approximating the (square) matrix A with its q largest principal components (basically using the rank-q...

Asked on 10/23/2021

1 answer

$P0$ elements for $H1$

Are there $P0$ (zero degree/constant element) nonconforming methods for approximating solutions in $H1$? More specifically, I have the equation: $$u-f - TDelta u = 0$$ Which can...

Asked on 10/23/2021

2 answer

Different questions about "Inverse Physics problems"

I am in a context of forecasts in astrophysics. Don't be too rude if questions seem to you stupid or naive but rather indulgent, I am just looking for better...

Asked on 10/23/2021

2 answer

Numerical solution of high-dimensional integral involving positive-part function

Consider a potentially high-dimensional (say, $N$ up to 20) integral of the form$$int_0^infty rho_1(x_1)rho_2(x_2) cdots rho_N(x_N) bigg(x_1+x_2+cdots+x_N -Kbigg)^+ , dx_1 cdots dx_N.$$where $(z)^+...

Asked on 10/23/2021

3 answer

Calculating the Strange Attractor of the Duffing Oscillator in C++

I am simultaneously trying to learn computational physics methods, chaos, and C++. I think this is the right site for the question, and I apologise if not. I started working...

Asked on 10/23/2021

1 answer

coarsening coefficient matrixes (A2h, A4h...) for geometric multigrid method in 2-D/3-D

I am learning about multigrid methods from the textbook section 6.3 Multigrid Methods, which shows a geometric multigrid algorithm for 1-D examples in detail, including how to...

Asked on 10/23/2021

1 answer

How to calculate error in successive over relaxation for PDE?

I am trying to solve the Poisson equation numerically using the FDM method in C++. But I have a little confusion with the iterative process. I understand that the number...

Asked on 10/23/2021

1 answer

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