All Questions

I am at an international conference (ICIAM2019) about numerical methods and am surprised by the prevalence of applications directly relatable to arms research. examples: One award winner holds his ...

My program loads a parallel PETSc matrix $A$ on several MPI processes, each holding a block submatrix $A_i$. I would like to retrieve the local submatrix $A_i$, the one corresponding to the current ...

I am trying to solve many different linear systems in parallel in matlab. The problem is, each linear system has entirely different parts and are fairly large, so passing the information to each of ...

I have the impedance matrix $Y$, formulated from an electrical network by augmented nodal analysis. The matrix $Y$ is shown as an image to illustrate its feature visually, where all the white blocks ...

I'm trying to solve the Nonlinear Schrodinger's Equation (NLSE) in 2D using Finite Elements, but I don't know how to handle the nonlinear term. I suppose I have to apply the Newton-Raphson algortihm ...

Does anyone have a intuitive explanation of why Hermite polynomials have to be utilized as the shape functions in the FEM solution of the Euler Bernoulli Beam 4th order ODE? I have been learning FEM ...

How to set the initial guess for the iterative solver GMRES or FGMRES for linear problems (Helmholtz equation of RF module) in comsol?

It was suggested I ask this question in this section. Anyway: I have a particular nonlinear PDE of the form $$ u_t(x,t)=iu_{xx}(x,t)+f(x,u(x,t)) \tag{1} $$ Where f is some nonlinear function. With ...

I've been developing a curvilinear FVM code. So far I've implemented the PPM scheme and am looking into adding WENO schemes. So far I've been discretizing the grid metrics using a second-order central....

I want to solve the following nonlinear system in 1D \begin{cases} \dot{R} + v \frac{\partial R }{\partial x} - \frac{\partial }{\partial x}\left( D \frac{\partial R }{\partial x} \right) -\Gamma =...

TLDR: Is there an efficient algorithm to compute the intersection of polyhedra with 8 or fewer vertices? I have two sets of FEM meshes for one geometry (one exhibiting a skin effect). I have to ...

I want to decompose a list of 3D vectors $X_j$ as linear combination of five 3D verctors $C_k$ $$X_j= \sum_{i=1}^{5}{w_{ji}C_i}$$ both $X_j$ and $C_i$ are 3 components vectors $$C= \begin{bmatrix} ...

I am currently working on remeshers for my simulations (academic purpose) and I try to find a method to remesh previous meshes using Ggmsh. The first mesh (normalMesh.msh) was created using a .geo ...

I'm trying to numerically solve a simple Laplace equation in 2D, with a nonlinear source term: $\nabla^2 u = u^2$ with boundary conditions as $u=0$ everywhere except for $y=1$ where $u=u_0$. I'm ...

This is a basic question. But I did not find any explanations for this. How are governing equations, like mass, momentum, energy conservations equations, different from 'Transport equation'?. Is a ...

$x$ is an $N \times M$ matrix. $y$ is a $1 \times L$ vector. I want to return "outer product" between $x$ and $y$, let's call it $z$. z[n,m,l] = x[n,m] * y[l] ...

I am trying to simulate strain propagation from the surface into the bulk. I have a rectangular semiconductor block (~2 μm thick) on top of which metal gates (~25 nm thick) are deposited as seen in ...

together! First of all, I have to mention that because of my background as an Industrial Engineer, I have limited abilities in mathematics, but am disciplined enough to expand myself from ...

I need to make the navigation and guidance of a vehicle (a quadcopter) in a platform. This platform can be seen like this: where the blue dots are the center of each square, and the $x$ distances are ...

The error estimates in FEM are usually of the form $$||u^h-u||\leq Ch.$$ Taking logarithm on both sides, we obtain $$\log ||u^h-u||\leq \log C + \log h.$$ This estimate implies that the error lies ...

I am using Python 3.7 to write a program that requires me to calculate the root of the Hermite interpolating polynomial, given two points $\epsilon_0$, $\epsilon_1$, the function ($d(\epsilon_0)$,$d(\...

I have a program, structured in two parts, $A$ and $B$. Both parts are capable of running as standalone units, and written in C++. $A$ is written for cluster systems, running entirely on CPU-nodes, ...

I have a simulation project written for OpenFOAM and CFDEM and would like to find an alternative to run it on GPU since raising the number of cores already provided a promising speed up and ...

I'm wanting to build a computer for scientific or big data computing (Python, Fortran, Matlab) and I was hoping to get some advice on the type of processor, memory, graphics, etc I would need. I ...

It seems to be very hard to use comsol to solve contact mechanics problems. Parametric solvers seem to be the only working solvers, followed by Static solvers. Transient solvers never work. Are these ...

, what does “D = diag(W.1)” means?on page #2, just below equation (6) PFA screenshot and here is the link of the paper - original paper

I would like to join several hexahedra and obtain an outline volume. First, I started with 2D implementation. In 2D, there are non-intersecting quadrangles which always touch each other as shown in ...

Mesh information like points, faces and cells is to be stored into separate files: e.g. for points file: # points data: x y z N_Points 100 x1 y1 z1 x2 y2 z2 ... cell file: # cells data: ...

I have a computer model with a number of parameters that need to be calibrated based on experimental results. It's also important to understand the sensitivity of the results to each parameter ...

I wonder if there is a fast algorithm, say ($\mathcal O(n^3)$) for computing the cofactor matrix (or conjugate matrix) of an $N\times N$ square matrix. And yes, one could first compute its determinant ...

I am writing a paper in which I want to cite the earliest reference to the augmented Lagrangian method in FEM. For the pure Lagrangian method in FEM, the classical work of Babuška [1] is the original ...

I am looking for a way to do local sensitivity analysis for PDEs, preferably in Python. I get the impression that discretizing the equation then treating it as an ODE could work; however, would that ...

I need to make a bilinear interpolation of a function Y(i,j) tabulated in a 100x100 grid. I tried with the fortran polin2.f and polint.f subroutines of Numerical Recipes. This routines seems to be ...

What is the difference between Probabilistic Latent Semantic Analysis(pLSA) and Latent Dirichlet Allocation (LDA)?

I got stuck with Hestaven/Warburton's dG-FEM Matlab code. Starting with the file AdvecRHS1D.m, we see in line 11 ...

I do not really get the point of null space usage for creating the prolongation operator for smoothed aggregation algebraic multigrid. I know what the null space is per definition and I know that the ...

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 ...

I have a set of integers (zeros and ones) describing a molecule. I need to create a matrix where all molecules are stacked together so each row is one set of integers (bit vector). My understanding is ...

I am having hard time learning the method of impulse based dynamics developed by Mirtich for rigid body dynamics simulation. Please help me out if any body has any example code(algorithm) of it. ...

In the book of Hesthaven and Warburton on discontinual Galerkin methods the authors give motivation to the differentiation matrix (page 52), referred to as $D_r(i,j)=\frac{dl_j}{dr}|_{r_i}$ where $l_i(...

I'm trying to figure out how to translate a piece of code from Velocity Verlet to Runge-Kutta, while treating the time step dependence of the thermal noise correctly. The Langevin equation for my ...

General question I work on the plane where I have a two-dimensional shape $V$ that is cut in a collection of parts $\{V_i\}$ that do not overlap $ V_i ~~\text{s.t.}~~ \bigcup_i \overline{V}_i = \...

I am trying to generate random numbers using Levy distribution in MATLAB. I am using the inverse transform method to generate random numbers and then plot its histogram for pdf estimation. Then I ...

Consider the regularized least squares problem $$ \min_x || b - A x ||^2 + \lambda^2 ||x||^2 $$ which is equivalent to $$ \min_x \left|\left| \pmatrix{b \\ 0} - \pmatrix{A \\ \lambda I} x \right|\...

I have a complicated equation that defines a shape in 3D, and I would like to generate a surface mesh. The shape is defined by an isosurface, i.e. the function is positive inside the shape and ...

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 ...

I have been trying to model the flow in a very thin channel using COMSOL Multyphysics. The laminar flow module does not converge no matter how I change the meshes, or use ramping loads and such. The k-...

My objective is to get a conformal surface mesh between two geometries meshed independently in different files. By example, I can start with a simple cube in one .geo file and mesh this geometry. ...

I am studying the following lecture (image) regarding 5 iterations of the simple RRT algorithm. I am trying to understand how each value is being updated regarding each iteration. I have figured out ...

I originally posted the question on the math stackexchange, and was told I should try here. I’m researching Stochastic PDE, in particular the Navier Stokes Equation, and would like to estimate the ...