All Questions

Filter by
Sorted by
Tagged with
0 votes
1 answer
24 views

(Isoparametric) Mapping of physical coordinates to their equivalent parametric coordinates on a reference element

I have some experiece with finite element methods (FEM), in general. However, I mainly worked with Cartesian grids -- i.e. using orthogonal (non-curved) elements. Recently, I became interested in a ...
debronee101's user avatar
0 votes
0 answers
24 views

1D FDTD simulation of plane wave propagation and the Courant stability condition

I'm currently trying to simulate a simple case of wave propagation in free space before adding in more complexities, and already I'm stumped. I understand the Courant stability condition. However, I ...
Jerry Y's user avatar
2 votes
0 answers
28 views

Good references for the P3/P1dc element

I am struggling to find some good references for the P3/P1dc element (cubic element for velocity and linear piecewise discontinuous for pressure) for the Stokes/Navier-Stokes equations. Is there a ...
Chenna K's user avatar
  • 964
0 votes
1 answer
43 views

Source for scalability challenge for number of finite element nodes per process

Context In distributed simulation of a finite element mesh with $N$ nodes and $P$ processes, a professor stated to me that "achieving good scaling for more than 25,000 finite element nodes per ...
Jared Frazier's user avatar
0 votes
0 answers
26 views

Fastest way to calculate the eigenvector with the largest eigenvalue for a 3*3 positive-definite matrix

As stated in the title: I have a 3 by 3 positive-definite matrix $M$. What I need is the eigenvector corresponding to the largest eigenvalue, since I am calculating the solution to maximize the value ...
Enigmatisms's user avatar
0 votes
1 answer
34 views

Estimating the rate of convergence of Projected Gradient Descent on constrained polynomial objectives

I am estimating the order of convergence of Projected Gradient Descent (GD) on quadratic polynomials with random coefficients independently drawn from Uniform(-1,1) and bounded by a unit hypercube. I'...
ufghd34's user avatar
  • 21
3 votes
0 answers
38 views

Datasets for inverse heat transfer problems

I was wondering if there is an available, real-life known inverse heat transfer problem dataset to benchmark oneselfs algorithm, as in MNIST for deep learning. Talking about... (well in this case I ...
Aner's user avatar
  • 181
1 vote
1 answer
43 views

Solving TOV equations that describes neutron stars in modified f(R, T) gravity

Sorry for the long post, tldr at bottom. I'm trying to use standard RK4 code in C/C++ to solve a coupled system of 2 modified TOV equations in f(R,T) gravity and reproduce some of the results of this ...
hidenori's user avatar
2 votes
2 answers
136 views

Finding ALL Eingenvalues of a Sparse Integer Matrix

I would like to find ALL Eingenvalues of a huge, very sparse integer matrix. This matrix has a lot of known properties, e.g. that it is symmetric and nearly tridiagonal, with very few (max. ca. 4 per ...
BernhardWebstudio's user avatar
0 votes
0 answers
56 views

How to correctly discretize volume elements in different geometries?

I am solving a reaction-diffusion problem in one dimension for a catalyst particle to get the internal effectiveness factor ($\eta$),as given below: $$ \eta = \frac{\int_0^{V_p}{R_i\ dV}}{R_i^{surf}\...
HWIK's user avatar
  • 23
0 votes
0 answers
33 views

Quettaflops in the palm of your hand [closed]

Quettaflops in the palm of your hand I bring to your attention the concept of a central processor that fits in the palm of your hand, costs a penny, and it is millions of times faster than all ...
Victor Konovalov's user avatar
0 votes
0 answers
30 views

Rule-Based Link Prediction for Social Network

Relevance to Site I believe this question is suitable for the Computational Sciences Stack Exchange site as it pertains to the implementation of a graph algorithm. According to this widely accepted ...
Jay Gupta's user avatar
5 votes
1 answer
336 views

Time integration of first-order ODE with higher-order information

Suppose I wish to derive a numerical integrator for the first-order ODE $$x'(t)=F(x(t)).$$ By differentiating both sides of the expression in $t$, I can write a second-order relation also satisfied ...
Justin Solomon's user avatar
9 votes
0 answers
133 views
+50

What's the most computationally efficient implementation of Kalman Filter

I know there are many formulations of the Kalman Filter. A few I can name are: Classical Covariance Form Informational Filter Form Square-Root Form or Factor Form But somehow it's hard for me to ...
CuriousMind's user avatar
2 votes
0 answers
113 views
+50

How to add damped constraint force to constrained dynamics simulation?

I have implemented a constraint dynamics physics simulation as proposed by Andrew Witkin et al 1990, but I cannot get the initial constraint "snapping" correctly. I implemented $$ JWJ^{T} \...
EmmanuelMess's user avatar
1 vote
1 answer
124 views

Coupled Partial Differential Equations

I'm trying to solve the following system of coupled differential equations, the two-temperature model for $e$ = electrons and $l$ = lattice. $$ \rho_{e}C_{p,e}\frac{\partial T_{e}}{\partial t} = k_{e}\...
clope99's user avatar
  • 11
0 votes
1 answer
78 views

optimize this python code that involves matrix inversion

So I have this line of code that involves a matrix inversion X = A @ B @ np.linalg.pinv(S) $A$ is an $n$ by $n$ matrix, $B$ is an $n$ by $m$ matrix and $S$ is an $...
Taylor Fang's user avatar
0 votes
1 answer
73 views

GMRES implementation does not converge for singular Hermitian problems

I've just implemented the GMRES algorithm based on chapter 4 of Fundamentals of Numerical Mathematics for Physicists and Engineers using the problems in Numerical Analysis by Timothy Sauer for ...
Olumide's user avatar
  • 317
1 vote
0 answers
11 views

Guidelines for image detection model for statis sample

I have 20,000 plus images of art (paintings, sculptures, jars, etc). My goal is creating a computer vision model that, from an input (image), identifies the exact same piece of art and returns its id, ...
Romina Silvera's user avatar
0 votes
0 answers
69 views

How can I get more accurate electric scalar potential in 2D closed box?

I am trying to use poisson equation to plot the electric scalar potential in close 2D space. The details in in this video and this one The following in written in Matlab for quick prototype. ...
kile's user avatar
  • 101
3 votes
0 answers
110 views

Quantifying the inefficiency of Gauss–Hermite quadrature

I am trying to understand the following part of the paper https://doi.org/10.1137/20M1389522 where the author argues about the inefficiency of Gauss-Hermite quadrature. I think I get the gist of the ...
Loik's user avatar
  • 31
2 votes
1 answer
273 views

Asking advice for implementation of Conservative Finite Difference Scheme for numerically solving Gross-Pitaevskii equation

I am trying to numerically solve the Gross-Pitaevskii equation for an impurity coupled with a one-dimensional weakly-interacting bosonic bath, given by (in dimensionless units): \begin{align} i \frac{\...
sap7889's user avatar
  • 21
0 votes
0 answers
37 views

Split RAM asked between nodes and different partitions

I'm using a Slurm-based HPC at my university to run memory-intensive software. I need to know if it's possible to distribute the required RAM across multiple nodes and partitions. My lab has exclusive ...
Zoranis's user avatar
1 vote
1 answer
201 views

Boundary Conditions on the Inlet and Outlet in a Discontinuous Galerkin framework

In the book Discontinuous Galerkin Method (DGM), Analysis and Applications to Compressible Flow by Vít Dolejší and Miloslav Feistauer, Springer, it is mentionned, in section 8.3.2 that deals with ...
L Maxime's user avatar
0 votes
0 answers
35 views

Solving for expectation using iteration in a implicit function

For a implicit function $V(k,l)$, taking $l$ as given and $k$ to be the only variable, $k$ is sampling from an unknown distribution and $\mathbb{E}k = \bar{K}$. Using Taylor expansion on $V(k,l)$ ...
Zuba Tupaki's user avatar
4 votes
1 answer
99 views

How can I efficiently find an anti-symmetric generator of a special orthogonal matrix?

Given a special orthogonal matrix $O$ (i.e: $OO^T = 1$ and $\det(O) = 1$), I am trying to efficiently find a matrix $X$ such that $O = e^X$ and $X = -X^T$ using Python (NumPy & SciPy). One obvious ...
Solarflare0's user avatar
1 vote
0 answers
72 views

Eigenvalue Problem with Pseudospectral Chebyshev Polynomials

I am solving a linear 4th Order Eigenvalue ODE (Euler-Bernoulli Beam): $$ {\frac{d^{4}w}{dx^{4}}} = - \alpha {\frac{d^{2}w}{dx^{2}}} $$ The method I used was to apply a truncated spectral expansion ($...
Chlorine Pentoxide's user avatar
0 votes
0 answers
52 views

What is the best finite volume method for the following equation?

I'm trying to create a partial differential equation that approximates 1-D climate in a rocky planet's atmosphere, which accounts for energy transport via radiation and convection. I am only ...
nicholaswogan's user avatar
1 vote
1 answer
82 views

How to run scipy.optimize.minimize with L-BFGS-B for maxiter (completely)

I want to run the below code for maxiter = 20001. I don't want it to stop by some default criteria. ...
Saif Ur Rehman's user avatar
0 votes
0 answers
40 views

Advanced computing on FPGA

I am an absolute beginner in the FPGA topic (so far I have only implemented a couple of simple logic gates in Verilog and simulated them in ModelSim). I studied digital electronics, logic elements, ...
ayr's user avatar
  • 131
0 votes
0 answers
40 views

How can I calculate ROC50 in python?

I need to calculate ROC50 for a classifier in python. The ROC50 value is defined as the AUC when the 50th true negative is found. I have tried setting the max fpr value for roc_auc_score in sklearn to ...
Jamie's user avatar
  • 101
1 vote
0 answers
41 views

How can I apply a mixed boundary condition to a multi-material heat transfer problem using Crank-Nicolson?

I am working on a mixed material model for a melting material and need to enforce both a Dirichlet and Neumann type condition at the interface. Subject to an external surface heat flux at the top of ...
ZebraEagle's user avatar
1 vote
0 answers
32 views

Imposing higher order finite difference schemes for boundary value problems on a finite interval

I have some questions. I'm going to assume everything is in 1d with a Laplacian operator. If I discretize the Laplacian operator using $p = 2a+1$ grid points with periodic boundary conditions, I ...
Cuhrazatee's user avatar
0 votes
1 answer
106 views

Is the NLP formalism sub-optimal for real-world problems

My home-brew optimization studies have raised yet another fundamental question. The Nonlinear Programming formalism, "minimize f(x) subject to inequality and equality constraints, and x ...
m4r35n357's user avatar
  • 329
0 votes
0 answers
56 views

On Newton-Raphson Method for Single Degree of Freedom Systems

I am trying to understand the geometric interpretation of the Newton-Raphson method as used in nonlinear structural mechanics. The fundamental governing equation of nonlinear structural mechanics is ...
frustrated_engineer's user avatar
2 votes
0 answers
83 views

What is fastest method for finding the minimum and maximum eigenvalues of a (possibly very large) symmetric matrix?

What is the best way to find the extreme eigenvalues - in order to find the spectral radius - of a general real dense symmetric matrix? Looking at similar questions e.g.: What's the most efficient ...
ufghd34's user avatar
  • 21
0 votes
0 answers
20 views

What is the most accurate way of computing the evaluation time of a neural network model?

I am training some neural networks in pytorch to use as an embedded surrogate model. Since I am testing various architectures, I want to compare the accuracy of each one, but I am also interested in ...
HWIK's user avatar
  • 23
4 votes
3 answers
133 views

Is there any matlab built-in function or libraries to calculate $\frac{d(\ln A)}{dA}$?

we can first conduct spectral decomposition of an positive definite isotropic tensor $A$ and then we can define $\ln(A)$, then we can define the frechet derivative of it, but how to calculate this in ...
YuerWu's user avatar
  • 191
5 votes
3 answers
187 views

Benchmark Neural Networks on High-Dimensional Functions

For a personal project, I am interested in benchmarking certain neural network architectures in the context of high-dimensional function approximation. Specifically, I am interested in continuous, ...
user82261's user avatar
  • 169
4 votes
1 answer
358 views

Non-uniform Gaussian spaced vector

I am working on a Fortran code that uses a uniformly spaced grid in two directions (x,y). Which works fine, but when I need to study a certain problem with good resolution, I need to increase the ...
Gundro's user avatar
  • 43
2 votes
1 answer
154 views

how to compute the rate of deformation gradient in finite-element context?

I am implementing hyper visco-elastic material models similar to those from Pioletti et al. see here There, a viscous potential, e.g $W_v = \eta [I_1-3]J_2 \quad \text{with} \quad J_2 = \mathrm{tr}(\...
Simon's user avatar
  • 185
0 votes
0 answers
41 views

representing firing rates of a neuron using delta functions [computational neuroscience]

I'm reading 'fundamentals of computaional neuroscience' by Thomas P. Trappenberg and was confused while reading about representing firing rates using direc delta functions. instantaneous firing rate ...
GunHui Moon's user avatar
1 vote
1 answer
191 views

Solving linear system of equations with constraints on unknowns

I would like to solve a system of linear equations $y=Uh$ for an unknown vector $h$, where I have a few constraints on some of the elements of $h$. The matrix $U$ is composed of a vector $u$ (length $...
Neuling's user avatar
  • 35
0 votes
0 answers
19 views

Thermo Hydraulic Mechanical modeling of energy wall slab in camsol multiphysics

I am currently working on a complex simulation project involving an energy wall slab, and I need assistance in accurately modeling and validating it using COMSOL Multiphysics. Here are the details of ...
Hizbullah's user avatar
3 votes
1 answer
155 views

Any FEM book recommendations that focus on stability and proofs on error bounds?

Everything from descrete stability proofs for steady state and time dependent problems. energy stability, stability of mixed methods, nonlinear problems, vector valued problems in fluid/structural/EM, ...
CuteCompute's user avatar
2 votes
2 answers
83 views

Getting singular matrices for lid driven cavity problem

I was trying to solve the lid driven cavity problem using the galerkin method with SUPG stabilization. I was using GMRES method as my solver and I am also getting a solution. And the solution looks ...
Priyanshu's user avatar
0 votes
0 answers
55 views

LBFGS-B initial gradients too high?

I'm optimizing a geometrical shape for electromagnetic performance. The shape is constrained with bounds, say between 0.2 and 0.8, whereas the parameters are all between 0.2 and 0.8. I am interested ...
James Li's user avatar
0 votes
0 answers
47 views

How to solve the heat equation using the spectral method (Chebyshev's differentiation matrix), with constant flux boundary condition on both sides?

I am trying to solve a 1d heat equation with a constant flux boundary condition on the right-hand side and a zero flux boundary condition on the left-hand side. I've gained a lot of insight from ...
Kazusa's user avatar
  • 1
1 vote
0 answers
44 views

Mathematica Package for validating effective string theory solution

I am asking for Mathematica package that given an input of: symmetric matrix $G_{\mu\nu}$, antisymmetric matrix $B_{\mu\nu}$ and a scalar function $\Phi$ will check whether it is a solution to the one-...
Daniel Vainshtein's user avatar
2 votes
0 answers
47 views

trust region method for linearly-constrained convex optimization

I'm interested in the problem of minimizing a convex function $f(x)$ for $x$ living in some Banach space $X$, subject to the linear constraint $Kx = g$ where $K : X \to Y^*$ for some other space $Y$. ...
Daniel Shapero's user avatar

15 30 50 per page
1
2 3 4 5
230