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49 views

Numerov method for Schrodinger equation

While learning about numerical methods for solving the Schrödinger equation I came across Numerov's method. I want to get the solution for the harmonic oscillator by alreading giving the eigenvalues. ...
1
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0answers
40 views

Does Boost provide a template implementation of the wedge product?

Does the boost C++ library implement the computation of the wedge product? The wedge product is mentioned here, but it is not very clear (to me at least) whether there is a template implementation of ...
1
vote
0answers
74 views

What's the more efficient way to solve this matrix equation?

This is intended to be a more generic question not about a specific system. Given a hermitian matrix $H(x_1,\dots,x_n)$ depending non-linearly on some real parameters $x_1,\dots,x_n$. We want these to ...
5
votes
1answer
44 views

Term for an small optimisation algorithm used as a subroutine

Is there a term describing a specialised solver which is used as a subroutine or a different, larger solver? For example, a gradient descent solver which, at each step, uses a line search to optimise ...
1
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0answers
15 views

Find all recurring subgraphs/patterns of maximal size in a single undirected, labeled, connected graph

I would like to identify all subgraphs of maximal size (maximum number of nodes) that are recurrent in a single undirected, labeled, connected graph. I provide exemples of input and expected output ...
-1
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0answers
18 views

Normal duration of DFT calculations on a monolayer

I'm going to ask this here since I cant seem to find an appropriate forum for quantum ESPRESSO. I'm a beginner at quantum ESPRESSO and using currently the BURAI 1.3 GUI for it. I'm only using an 8-...
0
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0answers
21 views

Automatic single point constraint

A lot of modern FE codes have an option called AUTOSPC. Examples are Nastran or Marc. I know that this option removes degrees of freedom to avoid a singular matrix system. But how to determine ...
0
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0answers
8 views

Universal formulation of adiabatic equations of state in compresible finite-volume simultions

I code some finite element solver which should work for broad variety of materials (i.e. gas, liquid, solid, plasma) and large span of compressions resp. densities. I want to simulate things like ...
0
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0answers
46 views

A non linear ode with boundary conditions at infinity

I want to solve the non-linear ODE $$\frac{d^2}{dx^2}y=a(y+y^3)$$ With the boundary conditions that $$\lim_{x\to \pm \infty} y(x) =0$$ I am not aware of any analytical method for solving this kind ...
1
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0answers
58 views

How can I solve the matrix optimization problem where denominator and numerator are different?

I want to solve the following maximization problem in $\mathbf{X}\in {\mathbb{R}}^{{m} \times {n}}$ \begin{eqnarray} \begin{split} \quad\max_\mathbf{X} \frac{\mathbf{Tr}(\mathbf{X}^\top \mathbf{Q} \...
2
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0answers
44 views

Can Taylor methods be used effectively on stiff ODEs?

Cleve Moler has stated that "all numerical methods for stiff odes are implicit." However, I don't know whether this statement is a mathematical fact, or an simply an observation. Moreover, many ...
1
vote
1answer
61 views

What will be the impact of quantum computing on existing numerical techniques (e.g. CFD)?

Quantum computing seems to be a very active and promising development area in computer science. However, I am curious as to what impact (if any) quantum computing will have on existing classical ...
1
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0answers
17 views

Tracking channel states using Machine Learning

I am new in AI and would like to apply machine learning to estimate the channel states. I have a set of data. It is a matrix of 10000*8. Each row of this matrix is regarding a time step, i.e., 1st row ...
0
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0answers
54 views

How to make this parfor loop work properly in Matlab?

I have a code that does some calculations for a given value p (p is between 0 and 1). In theory I should be able to make a parfor loop that runs over the values of p, with p being a vector (for ...
4
votes
2answers
105 views

Efficient algorithm to decide if a graph is a cactus?

A cactus is a connected graph in which every edge belongs to at most one simple cycle. How should one modify the Depth First Search algorithm to obtain an efficient algorithm that determines if a ...
2
votes
0answers
71 views

Partial differential equation with convolution integral

The GP equation is $$i\frac{\partial u}{\partial z}+\nabla^2u+|u|^2u+\int e^{-[(x-x')^2+(y-y')^2]}|u(x',y')|^2 dx'dy'u(x,y)=0$$ with Neumann boundary condition. The initial condition is given by a ...
1
vote
1answer
55 views

Activation function with special conditions in machine learning

I only have a basic understanding of deep learning, but looking through it I had an idea on how to approximate global minima of the NN. However, for it's activation function I am only able to use: ...
36
votes
5answers
6k views

Is it possible to have a career in SciComp without contributing to arms research?

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 ...
3
votes
1answer
40 views

PETSc - Manipulate BAIJ matrix locally

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 ...
2
votes
1answer
36 views

How to pass matrices to parallel workers quickly in matlab?

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 ...
1
vote
1answer
74 views

Sparse matrix inversion

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 ...
2
votes
1answer
111 views

How to use Newton-Raphson method to handle nonlinear terms in coupled system of PDEs?

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 ...
0
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0answers
57 views

Shape functions in Euler Bernoulli Beam Equation

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 ...
0
votes
1answer
73 views

How to set an initial guess for the iterative solver in Comsol?

How to set the initial guess for the iterative solver GMRES or FGMRES for linear problems (Helmholtz equation of RF module) in Comsol?
3
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0answers
68 views

Integrators for Nonlinear/Stiff PDE

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 ...
1
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0answers
45 views

WENO scheme on curvilinear coordinates

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....
2
votes
0answers
38 views

References to solve system of differential equations which describe the evolution of sandpile surface using the finite element method

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 =...
2
votes
0answers
43 views

Efficient algorithm to determine the intersection volume of simple convex polyhedra

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 ...
1
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0answers
37 views

least squared optimization

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} ...
1
vote
1answer
56 views

Is it possible to remesh with gmsh?

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 ...
0
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0answers
31 views

Why does GMRES converge much slower for large Dirichlet boundary conditions?

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 ...
1
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0answers
49 views

Governing equations vs Transport equations

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 ...
2
votes
1answer
34 views

numpy.outer without flatten

$x$ 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] ...
3
votes
0answers
48 views

Strain propagation from surface to bulk in COMSOL

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 ...
3
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0answers
20 views

Sequence planning with 3 machines

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 ...
8
votes
1answer
168 views

Should we always expect FEM error plots to be straight lines?

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 ...
3
votes
1answer
54 views

Get the roots of a Hermite interpolating polynomial

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(\...
2
votes
0answers
35 views

Best way of porting code from the GPU to MPI-nodes

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, ...
0
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0answers
39 views

OpenFOAM and CFDEM on GPU

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 ...
0
votes
1answer
74 views

Computer build for scientific or big data computing [closed]

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 ...
0
votes
0answers
33 views

contact mechanics in COMSOL

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 ...
0
votes
1answer
50 views

what does “D = diag(W.1)” means?

, 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
2
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0answers
33 views

Algorithm to join hexahedra and obtain outline volume

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 ...
0
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0answers
63 views

How to read data from simply formatted text file (c++)?

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: ...
0
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1answer
88 views

How to optimize sampling for parameter estimation

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 ...
4
votes
1answer
65 views

Fast algorithm for computing cofactor matrix

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 ...
4
votes
1answer
87 views

Original paper on the augmented Lagrangian method in FEM

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 ...
1
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0answers
71 views

How to perform local sensitivity analysis for partial differential equations

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 ...
1
vote
2answers
56 views

bilinear interpolation for large grids

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 ...
1
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0answers
16 views

difference between PLSA and LDA

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

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