All Questions

Suppose if we take $X_h(G)$ as finite element space then this space (space of piecewise constant basis function)is defined as $$X_h=\{v: v|_{T}=c_{T}, T \in \mathbb{T}\},$$ where $\mathbb{T}$ is a ...

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{...

Say the model is $F(x_1)G(x_2)Z(x_3) = y \in \mathbb{R}^N$, with $F,G,Z$ explicitly known, we are given observation of $y$ as $y_b \in \mathbb{R}^N$ to find the value of $x_1$, $x_2$, $x_3$ for each ...

I'm trying to include a "great M" penalty in my objective function. I want use the entry x vector values as entry values in a function. A fixed maximum value is took initially for the returned value ...

I need to find the cubature rule for the following integration $$\int_{S^{2}} f(s,\tilde{s})d\tilde{s} ds,$$ where $S^2$ is the unit sphere in $\mathbb{R}^{3}$.

I have the following convolution as part of a numerical simulation. $$T(r)=\int d^3r_2 p(r_2)f(r_2)\alpha(r-r_2)$$ My problem is that the analytical expressions for $f$ and $p$ do exist but, I have ...

Suppose $f(x,y)$ is a complex function of two real arguments with roots* that are not discrete points but lie in curves. (Is there are term for this characteristic?) An example is shown below: the ...

I am using the reduced chi-squared statistic to determine the goodness of fit. I run several simulations and determine that a parameter 'p' has a certain range of values that all give values between 0....

My simulation, written in C++, generates a large amount (roughly ~500) of text files for each set of parameters I try to simulate, with four columns of ~5k double values in each file. Furthermore, to ...

I am studying how to speed-up the BFGS method using quantum computing techniques. I have used a method of speeding up the gradient of the function, but it sacrifices the precision value of the ...

I'm trying to define a MINLP optimization problem with GEKKO in Python, and I want to use some variables with fixed values. For my first variable, x1, I need to define the following values (as would ...

The problem I'm trying to make a metropolis simulation of the 2D Ising model. Basically, it's the following, for each monte-carlo step: Visit each lattice site, Compute energy required to flip ...

I'm trying compute the heat capacity $C_v$ out of my simulation for the 2D-Ising model which is given by $C_v = \frac{\langle E^2 \rangle - \langle E \rangle^2}{T^2N^2}$ ($E$: Energy, $T$: ...

The usual story of Givens rotations vs Householder reflections is that Householder reflections are better if you want to map a long vector to $e_1$, while Givens is better if you want to map a 2-...

I have essentially periodic data from a simulation (not exactly periodic but is qualitatively fairly periodic), and I'd like to take an average or noise filter of some sort that I can get a well ...

I am a graduate student majoring scientific computing. The numeric model I made caused a very ugly-looking saddle-point linear system. It is not symmetric at all and I will attach the sparsity pattern ...

I was curious if there was any software (preferably in C++, Java, and/or python) that could be used to simulate the following: Heat capacity of a fluid Heat transfer through a liquid and a solid ...

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

My problem is the following : I found the ground state energy (for the Ising model) with neural networks (more specifically RBM). I reproduced the same result but by increasing every time the ratio $=...

I have set of N m-dimensional vectors $\{\phi_i\}$ which gradually loose mutual orthogonality in an algorithm. => I have to re-orthogonalize them every few iterations. But if I do e.g. Gram–Schmidt ...

The scheme is given by $$\frac{v_m^{n+1}-v_m^{n-1}}{2k} + b\frac{v_m^{n+1}+v_m^{n-1}-v_{m-1}^n-v_{m+1}^n}{h^2} = 0$$ where $v_m^n$ is the numerical solution at the $m^\text{th}$ spatial coordinate ...

Is it necessary to reorder nodes (using Reverse Cuthill-Mckee algorithm, for example) if I am already using a CSR or CSC storing technique? Because since CSR/CSC stores only non-zero elements I guess ...

I'm struggling to find a good detailed reference explaining the Arc-length method or, more generally, Riks method and its derivations. I looked for the classical books in nonlinear mechanics (the ones ...

Let x, y be two floating-point numbers. What's the right way to compute their mean? The naive way ...

I am attempting to replicate results from this article. I'm not sure why but my results are completely different and wrong. For example, the exact solution with parameters ($x=0.1$, $T=0.01$, $Re=0....

I want to discretize the following equation using a Finite Volume Method $$\nabla \cdot (a(x)\nabla u)=f(x)\\x\in \Omega \subset \mathbb{R}^2 \\u_{|\partial\Omega}=g$$ I'm using Voronoi cells here: ...

I would like to solve the following differential equation numerically in 2D, $$\frac{\partial z^-}{\partial t}+(\vec{B}\cdot\vec{\nabla})z^-=0,$$ see Wikipedia if you are curious about what the ...

I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...

I need to estimate $$ \mathbb{E}_x[f_i(x)] = \int_{\mathbb{R}^n} f_i(x) p(x) dx $$ for many functions $f_i(x)$, where $p(x)$ is the density of a normal distribution. The evaluation of all the ...

In C programming language, if I allocate char buffer[2], but I store inside buffer something bigger (for example size 5), using for example buffer[4]=3; the program does not crash. Is it normal ? ...

I am numerically solving a nonlinear wave PDE using the Runge-Kutta method, and I know the solution I am looking for is constant in time, but I do not know the solution. What is a good way of ...

Excuse my lack of vocabulary for I have no formal training in this field, which is also why I ask this question - it may be trivial or it may be impossible. I want to evaluate an expression in the ...

I have the following convex optimization problem. I would like to ask is there any efficient way to solve it in Python? Can I use CVXOPT package? If so, any detailed instruction? Thanks a lot. $$ \...

I have $x$ and $y$ data, both of which have their own covariance matrices. scipy.optimize.curve_fit will accept a covariance matrix for the $y$ data, called ...

I am trying to solve Lid driven square cavity flow problem of Stokes equation using finite element method. I have boundary conditions for velocity as zeros on every boundary but u=1 on top boundary. ...

I want to simulate a diffusion environment given by the differential equation $$\frac{\partial u(x,y,t)}{\partial t}=D\left(\frac{\partial^2 u(x,y,t)}{\partial x^2}+\frac{\partial^2 u(x,y,t)}{\...

Is there an efficient way to form this block matrix with numpy or scipy? $$ \left[ \begin{array}{cccc} \mathbf{B} & \mathbf{0} & \cdots & \mathbf{0}\\ \mathbf{AB} & \mathbf{B} & \...

I'm trying to improve the speed of the following iteration to calculate $s_k$: $$B_k^{-1} = \Bigg( I + \frac{s_{k}s_{k-1}^T}{||s_{k-1}||^2}\Bigg)...\Bigg(I+ \frac{s_1s_0^T}{||s_0||^2}\Bigg) B_0^{-1}\\...

I am solving an advection-diffusion equation using the FEM and am having trouble calculating my fluxes. I start with the equation, $$\frac{\partial n}{\partial t} = \frac{\partial j_{n}}{\partial x}\...

I found that a lot of my computational science programming has testing requirements that are not covered by standard test frameworks: Computation time testing To make sure that algorithms don't get ...

I've asked this question on mathoverflow too. Let $T>0$ $I:=(0,T]$ $d\in\mathbb N$ $\Lambda\subseteq\mathbb R^d$ be nonempty and open, $$\mathcal V:=\left\{\phi\in C_c^\infty(\Lambda,\mathbb R^d):...

I have a .csv file of thousands of (x,y,z) point particles that I would like to visualize in ParaView. I am able to plot a 3D scatterplot using the TableToPoints, and by decreasing point opacity I can ...

I am trying to solve the Helmholtz equation with Robin boundary conditions with complex coefficients and the weak formulation $$ \iint_\limits\Omega\nabla p_0(x,y)\nabla\left(\overline{v(x,y)}\right)...

In OpenFOAM by default, the FireFOAM is well supported for solid pyrolysis modeling. With that in mind, I managed to built my solver for a modified version of pyrolysis (for dry coal - without ...

Optimizing two models here, each model having its own set of parameters and an objective, but both models run on the same data which is difficult to compute, and which is computed based on both models'...

My plan is to solve the heat equation in the right half portion of the domain, while having the left half completely isolated with constant temperature. To do so, I model the left half with a very low ...

I'm developing a finite volume solver for the simple twodimensional advection equation with constant velocities $u, v$ and constant mesh spaces $\Delta x$: $$ \frac{\partial \rho}{\partial t} + u \...

Is it possible to solve an equation with only a single derivative such as: $$\frac{\partial U(x,t)}{\partial t} = A - BU(x,t)$$ with finite difference methods? I ask as I am trying to solve the ...

Context: I am working on implementing this paper and I am struggling to come up with a variational formulation for the Butler-Volmer interface conditions. To simplify my question I consider the ...

I am using the C++ library ODEint, which is part of Boost, to solve an extremely large system of coupled ODEs - in particular 1975 equations with large rational functions in the coefficients. In the ...