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1answer
29 views

Does mass balance hold in convective diffusion

I'm trying to understand how convection-diffusion equations are solved in pipe flow modules available in CFD solvers. $$ \frac{\partial C}{\partial t} + \nabla \cdot (\mathbf{v} C) = \nabla \cdot (D \...
4
votes
1answer
85 views

Complex differentiation of linear solvers

I have a linear system $$Ax=b$$ which I'm solving approximately, and I need to take the frechet derivative of x with respect to z. Were I solving the problem exactly (either analytically or to machine ...
3
votes
1answer
62 views

Recommendation for a fixed-step ODE solver?

My problem involves the solution of a second-order ODE with a fixed-step (input and output). Specifically, this ODE is the radial part of Dirac and Schrödinger equation for a spherical symmetric ...
2
votes
1answer
88 views

Modified Equation and Stability for Centred Finite Differences for Wave Equation

I am trying to use the modified equation to derive the stability condition for the finite difference approximation $$ \frac{u(x,t+\Delta t) - 2 u(x, t) + u(x, t -\Delta t)}{\Delta t^2} = c^2 \frac{...
1
vote
3answers
473 views

Create mesh for complicated 3D object for finite element analysis

I see images of steel connections, concrete dams, and other complicated 3D objects in papers which finite element analysis has been performed on them. My questions are: How these objects are created ...
1
vote
1answer
78 views

Numerical solution to the Landau-Zener problem

I tried to use a midpoint method and numerically solve the Schrödinger equation for the original Landau-Zener (LZ) problem: a $2\times 2$ Hamiltonian $$\left(\begin{array}{c} \alpha t\\ \delta \end{...
-1
votes
0answers
23 views

Multi-domain 3D Geometries for MATLAB PDE Toolbox

I'm seeking to use the PDE Toolbox within MATLAB to solve for the 3D anisotropic magnetostatics equation for the vector potential: $ \bigtriangledown \times \mathbf{v} (\bigtriangledown \times \...
10
votes
2answers
379 views

What guidelines should I follow for simulation software projects?

I am not sure whether this question belongs here, but I would like to give it a try and benefit from the experience of the people at scicomp.SE. From my experience, the software quality in ...
6
votes
0answers
83 views

fastest way to compute many small dot products

I have two n-by-3 blocks contiguous in memory ("n vectors of length 3") and I'd like to compute the dot product between each of the rows as fast as possible. In numpy, using ...
2
votes
1answer
23 views

Does the k-th approximate solution of a stationary iteration belong to the k-th Krylov subspace?

For an stationary iteration method solving $Ax=b$ as follows: $$ Mx_k = Nx_{k-1}+b, $$ I have known that when $M = I$, i.e., the Richardson iteration, the k-th solution $x_k = x_{k-1}+r_{k-1}$ is in ...
1
vote
1answer
21 views

What is the standard, extrapolation, and modified version of Richardson iteration method?

I have been studying the iterative methods recently. For classical iterative methods solving $Ax=b$, I have seen that the most simplest iteration method is the so-called "Richardson iteration". But I ...
1
vote
1answer
289 views

Suitable finite difference method for a convection-diffusion system?

I am trying to solve a system of PDEs $H_{t} = \frac{0.3}{0.7} - \frac{0.005 B f(h(H))}{\theta} - \frac{0.3 f(h(H))}{0.7} + \frac{500}{0.7} (HH_x)_x + (HH_y)_y$ $N_t = \frac{N_{in} - 0.002 [N] B f(h(...
2
votes
1answer
45 views

What method to solve a sparse complex symmetric (non-Hermitian) system?

I have a sparse system (about 78% of zero entries) that is complex and symmetric (but not Hermitian). The following figure shows the structure of the problem. The off-diagonal blocks are incidence ...
-1
votes
1answer
24 views

How to use natural logarithm inside Expression

I'm trying to evaluate the exact solution of heat diffusion in circular plate. I'm not able to use the natural logarithm inside expression. ...
2
votes
1answer
69 views

Why Krylov subspace iterative methods are faster than classical iteration?

This semester, I have been studying the most popular iterative methods, i.e., Krylov subspace iteration methods. For a large sparse system linear $$ Ax=b, $$ where $A$ is nonsingular, I know that ...
0
votes
0answers
20 views

Can't plot correctly precession of perihelion of Mercury in MATLAB using ode45 or ode23

I was trying to plot precession of perihelion of Mercury using matlab. For this I am following a book Computational Physics by Nicholas J. Giordano and Hisao Nakanishi 2nd Edition. In that book ...
1
vote
0answers
39 views

FVM vs FDM vs Conservative form vs Non conservative form

My question is regarding solving the conservative form and the non-conservative form of the governing-equations (GE), like continuity or the navier stokes equation, using finite difference method (FDM)...
5
votes
0answers
100 views

Is a complete bacteria simulation with an exascale supercomputer possible?

Will it be possible to simulate a complete (at least simple) bacteria atom by atom on an exascale supercomputer? or is it possible already today with the largest systems? Here, I've read that ...
19
votes
1answer
2k 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 ...
1
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0answers
6 views

Find index for submatrix with maximum sum

Given an N-dimensional matrix A, I want to find an M<N dimensional index array I such ...
1
vote
1answer
44 views

Draw contour line to represent multiple contours

I have 5 data sets, each includes multiple scatter points. If I use the geom_path function in R, I could obtain 5 contours like the following graph shows. Those five contours are annotated outlines ...
0
votes
0answers
18 views

Truncated power series algebra implementation

1) I am looking for references for an efficient implementation and usage of TPSA. What sources exist besides Berz's 1989 original paper and the incomplete chapter in Dragt's book? 2) Are there ...
-1
votes
0answers
34 views

What precautions should be taken when using 2D Perfectly Matched Layers?

I'm solving linearized Navier-Stokes equations with Perfectly Matched Layers in two spatial directions $x$ and $y$, but in the time-harmonic frequency $\omega$-domain, which is meant to be less ...
2
votes
0answers
29 views

Solving long time averaged chaotic nonlinear equations

I have a modified chaotic equation of the form: $$\frac{\partial u}{\partial t} = - (u+c)\frac{\partial u}{\partial x} - \frac{\partial^2u}{\partial x^2} - \frac{\partial^4u}{\partial x^4}$$ I am ...
13
votes
2answers
3k views

Options for solving ODE systems on GPUs?

I would like to farm out solving systems of ODEs onto GPUs, in a 'trivially parallelisable' setting. For example, doing a sensitivity analysis with 512 different parameter sets. Ideally I want to do ...
2
votes
1answer
60 views

MATLAB's ode45 not dealing with initial conditions well [RESOLVED]

*Concern highlighted in yellow *Solution at bottom I have a differential equation to solve for the motion of an electron: $$ \frac{d^2v}{dt^2} = \frac{1}{\gamma^6}\left( \frac{eE}{\tau m} - \left( \...
1
vote
0answers
19 views

Using nondimensionalization to solve an ode in MATLAB [duplicate]

I am trying to solve an ode that uses some extremely large numbers and some extremely small numbers, namely $$ e = 1.6\times 10^{-19}\\ E = 10^6\\ \tau = 6\times 10^{-24}\\ m = 9.1\times 10^{-31}\\ c ...
2
votes
1answer
24 views

How to store all solutions of an ODE on Matlab for multiple values of a parameter

I would like to solve an ODE for multiple values of the parameter p and most importantly, save all the solutions for all the different values. Till now, I have ...
2
votes
0answers
11 views

What is the correct way to calculate deviatoric stress tensor in lattice Boltzmann method?

Due to my previous question, where I asked about flux calculation in lattice Boltzmann (LB) method here, I have more or less same question for deviatoric stress tensor calculation due to pseudo-...
0
votes
1answer
69 views

How do I get power from gaussian beam numerically?

I would like to get the power from a Gaussian beam given a set of points at which electric field is evaluated. Please follow my reasoning and tell me what assumption maybe are wrong Power definition ...
1
vote
1answer
60 views

Why do not we choose the error solution norm as an iterative method's criterion?

For solving linear system $$ Ax=b, $$ using iterative mehods, we often use the terminate criterion as follows: $$ \frac{\|r_k\|}{\|r_0\|}=\frac{\|b-Ax_k\|}{\|b-Ax_0\|}<eps. $$where $x_0$ is the ...
2
votes
0answers
44 views

What is the fastest algorithm for computing log determinant?

I am diving into some literature to understand which is the best algorithm for computing the log-determinant of a PSD matrix. So far I have found the following two papers: Large-scale Log-...
3
votes
3answers
66 views

CPU usage when a MPI rank waits during a blocking communication

A typical way of dealing with I/O in MPI parallel programs is to either read all data to a single node and dispatch to the other nodes accordingly, or send all data to a single node and write from ...
1
vote
0answers
25 views

What kind of problem or matrices are suitable for multigrid method?

For Poisson or Convection-diffusion equation as follows: $$ -\Delta u=f,\qquad u|_\Omega = g. $$ or $$ -\Delta u +\vec{w}.\nabla u=f,\qquad u|_\Omega = g. $$ using FDM or FEM discretization, we can ...
-1
votes
1answer
18 views

Plot sinewave on ZX axis [duplicate]

I am trying to plot a sinewave with a bit of 3d perspective along the ZX axis instead of the XY axis. I have so far been unable to get anything that works, and have been unable to locate any examples....
-1
votes
0answers
11 views

Norm of mixed constant/cvxpy variable array in cvxpy

I'm trying to incorporate a norm in cvxpy of an array that includes a constant and a cvxpy variable. Looking at something like: ...
0
votes
1answer
33 views

A lot of identical staff in Comsol material database?

I got a lot of elements in Material Browser of Comsol Multiphysics of Optics section. ...
0
votes
1answer
46 views

Solving differential equation in Python with discretized variable coefficients

I am trying to solve a differential equation with discretized variable coefficients which are calculated from a time serie. In this case the Runge-Kutta step size is fixed by the frequency in the time ...
1
vote
0answers
44 views

Using MATLAB to simulate the Ising Model

I am using MATLAB to simulate a 1D Ising Chain. I am running into an issue where when trying to find heat capacity, my system has a tremendous amount of noise. I'll post my code and an image of the ...
2
votes
0answers
26 views

Piecewise-linear Continuations vs Marching Squares/Cubes

It seems that both piecewise-linear continuation and marching squares are methods to produce iso-contours of a scalar function given the function's values on a grid. It seems that piecwise-linear ...
4
votes
1answer
1k views

Minimal surface solution in Python

Note: this question was also posted in StackOverflow and math.stackexchange. I have a set of 3D points defining a 3D contour, as shown below. The points in this contour lie in their best-fit plane ...
36
votes
11answers
2k views

Venues for publishing papers that emphasize software

Software is a fundamental part of computational science, and is increasingly recognized as an essential part of the scientific record. Given the value of using existing and well-tested code, it seems ...
5
votes
2answers
105 views

Is the diffusion equation with Neumann and Dirichlet BCs well-posed?

I am considering the following diffusion equation: $$\frac{\partial f}{\partial t} = \frac{\partial}{\partial x}[D(x,t)\frac{\partial f}{\partial x}]$$ over a grid ...
-4
votes
0answers
26 views

Derive the Finite Difference equation corresponding to the steady state PDE. Explain how to implement Dirichlet and Neumann boundary conditions

A rod of length L = 1m, is made of copper, with thermal conductivity κ = 380W/m/K. A uniform heat supply h = 10kW/m3 is applied to the rod. The left boundary of the rod is kept at constant temperature ...
1
vote
0answers
32 views

Question regarding 1D implementation of the DG method

I'm pretty new to the DG method and have been writing a 1D code to help me understand the coding aspect. With respect a reference, I've been following these notes https://www3.nd.edu/~zxu2/...
2
votes
3answers
102 views

Is there any other sparse matrix data in matlab built-in file?

I want to do some numerical examples solving large sparse linear system Ax=b. And I want to use some data from Maltab itself because this experiments are easily ...
3
votes
1answer
122 views

Consumer hardware for scientific computing?

I'm interested in problems around probability, statistics, and statistical mechanics, and often I find it useful to perform simulations to get some sense of the underlying phenomena. Example ...
12
votes
3answers
528 views

Fitting Implicit Surfaces to Oriented Point Sets

I have a question regarding quadric fit to a set of points and corresponding normals (or equivalently, tangents). Fitting quadric surfaces to point data is well explored. Some works are as follows: ...
3
votes
0answers
58 views

Numerical integration with singularity term

In https://www.johndcook.com/blog/2012/02/21/care-and-treatment-of-singularities, the author explains the subtraction method to get rid of singularities when performing numerical integration. The ...
4
votes
1answer
61 views

Is operation count a reliable predictor of performance when comparing two formulations?

I have two formulations to solve a problem (both give dense, complex and symmetric system). They are solved multiple times in a loop. I am trying to predict which is better to use. The first one ...

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