All Questions

I am implementing a logarithmic quantizer which is defined as follows: $$ q(u) = \begin{cases} u_i , \frac{u_i}{1+\delta} < u < \frac{u_i}{1-\delta} \\ 0 , 0 \leq u \leq \frac{u_o}{1+\delta} \\ -...

I have an optimization problem, which is to maximize the following integral over the unit sphere: $$ \max_B \int d\Omega \mathbf{f}^{\dagger}(\theta,\phi) (B^{\dagger} + B) \mathbf{f}(\theta,\phi) $$ ...

Every real matrix $A$ can be reduce to real Schur form $T = U^T A U$ using an orthogonal similiary transform $U$. Here the matrix $T$ is quasi-triangular form with 1 by 1 or 2 by 2 blocks on the main ...

Let $M_n(\mathbb{R})$ denote the set of $n\times n$ matrices with real entries. I have an $n\times n$ matrix $X\in M_n(\mathbb{R})$, and I would like to implement the linear operator $[X, \cdot] : M_n(...

I am trying to perform the following integral $$\int_{0}^{2\pi}\int_{0}^{+\infty} \frac{r'\left(e^{-r'^2/2\sigma^2}\right)\left(r-r'\cos(\theta-\theta')\right)}{r^2+r'^2-2rr'\cos(\theta-\theta')}dr'...

I am studying about the 1D EM-PIC (Electro Magnetics using particle-in-cell) simulation. I want to have a simultaneous time-integration of the electric/magnetic fields plus the motion of free charges ...

I'm writing a code for solving PDEs through the finite element method. In particular, I'm facing with 3D problems, in which I don't know how to calculate shape functions derivatives on the boundaries (...

I am looking for MCMC codes with a GPU suport (like NVIDIA or OpenCL libraries) to make faster run chains. I know there is a plenty of codes that does MCMC but which ones could allow to exploit GPU ...

I'd like to know how to deal with a divergence when trying to solve the Poisson equation for electrostatics with a simple spectral method. I'm not sure how to best state my problem, so I'll explain ...

I would like to calculate the number of floating point operations (Flops) my code is performing in my machine. To do so, I would like to be sure I am counting the operations in the inner-most loop ...

I would like to find the contours of a scalar function $u(x,y)$ available as a discrete set of function values $u_i = u(x_i,y_i)$ over a scattered set of points $(x_i,y_i), i=1,...,N$. In my case, the ...

I have applied SciPy's implementation of the Cuthill-McKee algorithm to a $48 \times 48$ sparse non-symmetric matrix in Compressed Sparse Row (CSR) format and the output is an array of length $48$ ...

I am trying to reproduce the results from the hp-VPINN paper (https://arxiv.org/pdf/2003.05385.pdf) on tensorflow (v1) for Poisson's equation, particularly the two-dimensional Poisson equation. In one ...

I tried to implement the 2d advection problem with a velocity field, that is not constant in space. My problem is, that the "mass" of my shifted density gets "eroded" or just ...

I have a 3D diffusion equation that I want to solve using a time splitting (2D+1D). Assume that $A$ is the 2D discrete diffusion operator and $B$ is the 1D discrete diffusion operator. I want to use a ...

I am working on implementing the Fourier beam propagation method in C++. I am really more of a programmer than a physicist but I think I have a good understanding of what I am trying to do. Here is ...

As we all know, the Additive Schwarz approach can be used as either solver or preconditioner, however, my question is, what is the difference between the two? In other words, how to use AS as solver, ...

How to compute 2-norm or infinity norm of following system? i am confused whether to calculate using simple matrix theory "where it don't regard for s domain" or H2 and H-infinty norm. ...

Context Let's say I am trying to model the spread of mold in a petri dish, using a stochastic cellular automata approach. The petri dish can be thought of as a grid of 1mm x 1mm squares, each called ...

I am trying to numerically solve equation (6) of Lakhina 2021 in Python. The equation is $$\frac{1}{2}\left(\frac{d \phi}{d\xi}\right)^2 + S(\phi, M) = 0\, .$$ The Sagdeev potential expression is ...

I am an amature in python, I wrote a simple code in jupyter. But it is giving an error. I want to plot a function: ...

The goal is to find vectors $x_u$ and $y_i$, both of the same length $f=64$, and to do this the following loss function is minimized: $$\sum_{u, i} (1 + \alpha \cdot r_{ui})(p_{ui} - x_{u}^{T}y_i)^2$$ ...

I'm searching for lower bounds of bilinear forms arising in FEM for elliptic second order PDEs with mixed boundaries. I did some research and found: $$\max_{v_{h}\in\mathcal{V}_h(\mathcal{\Omega})}a(...

I am using COMSOL to solve a mathematical model involving thermoelectric hydrodynamic (TEMHD) flow. I am running a very large parameter sweep and using the solutions obtained to make some plots. ...

I am looking for FOSS code that can generate self-avoiding random walk trajectories on a tetrahedral lattice. The purpose of the exercise is to create random conformations of model polymer chains that ...

I have a positive matrix $\rho \in \mathbb{R}^{n,n}_+$ as a discrete probability density. Furthermore, I have a tensor $u \in \mathbb{R}^{n,n,2}$ that is constant in time and acts as a vector field. I ...

I have seen in some papers that the energy levels in some arbitrary potential are specified. How can one find the energy levels in such arbitrary potentials. For example, $V(x)=\sin^2(x/2)$ with $x\in[...

I have written Poisson solvers using two different methods: A classic Jacobi scheme and one using the multigrid solver Hypre. I made up a couple of test cases ensuring the validity of those solvers. ...

Method of Moments and Finite Element Methods are two of the most used methods in computational electromagnetics to solve electromagnetic equations. As it is known, in FEM sparse matrixes are used ...

This question is a follow-up of this previous one. In "Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems" by Georgoulis et al., an error estimator is ...

I am trying to solve numerically the following 1D EBM: $C\frac{\partial T[x,t] }{\partial t} - \frac{\partial }{\partial x}\left ( D(1-x^2)\frac{\partial T[x,t] }{\partial x} \right ) + I[T] = S[x,t](...

is anyone here aware of whether there exist bounds on the optimal bandwidths of 2D/3D FEM stiffness matrices? Edit: more specifically, I would like to have bounds on the minimum bandwidth after ...

I recently had a software engineering interview and was asked a series of questions that was a bit outside of knowledge realm, and I feel like there's some scientific computing principles here (I took ...

When you're multiplying sparse matrices against other sparse matrices or dense matrices, what is the conventional approach for each? How are the sparse matrices stored? What does matrix multiplication ...

I am parallelizing code to numerically solve a 5 Dimensional population balance model. Currently I have a very good MPICH2 parallelized code in FORTRAN but as we increase parameter values the arrays ...

I met a problem in solving a set of coupled differential equation, as shown below: $$A_1\psi_1(z)+A_2\frac{d^2\psi_1(z)}{dz^2}+A_3\frac{d\psi_2(z)}{dz}=\lambda\psi_1(z)$$ $$A_4\psi_2(z)+A_5\frac{d^2\...

I have the nonlinear PDE $$\frac{\partial U(z,t)}{\partial t} + A(U)\frac{\partial U(z,t)}{\partial z} + B(U)U(z,t) + C(z,t) = 0,$$ where $A(U)$ and $B(U)$ are guaranteed to be real and positive. I ...

I'm studying an error estimator for the equation $\nabla\cdot(\beta u) + cu = f$ and it contains the following term $$||f - cU_h - \Pi(f-c U_h) ||_T$$ where : $\Pi$ is the local orthogonal $L^2$ ...

I am familiar with Cholesky decomposition and LU factorization for solving systems of linear equations. I have a problem where I have large sparse matrices (say, 1000x1000 or larger) where only one or ...

I have a short question about Time evolving block decimation (TEBD). During a lecture I was told that this method is very efficient in evolving 1D quantum spin systems with only nearest neighbor ...

Before I get to the heat equation I'd like to talk about the advection equation. Descritize that with FD in time and BD in space: \begin{equation} \dfrac{u^{n+1}_i - u^{n}_i}{\Delta t} + v \dfrac{u^{n}...

I've always had this question in mind (even if it may sound vague), but in my numerical analysis courses we've always learned how to analyze and optimize code. However, since most linear algebra ...

In some scientific papers I see that authors provide what type of simulation tool and what type of computer was used for computation. For example: The computations were performed using MATLAB in ...

In the finite element method we need to know a base for the fem spaces. For example, a base for the space $P_1(\hat{K})=<\{1-x-y,x,y,z\}>$ is a typical base for the polynomials of degree less ...

I was just curious as to why high-order (i.e. greater than 4) Runge–Kutta methods are almost never discussed/employed (at least to my knowledge). I understand it requires greater computational time ...

Many dense linear algebra decompositions (QR, SVD...) on an $m\times n$ matrix have cost $$ O(\max(m,n)\min(m,n)^2) $$ when implemented in practice on a computer. Is there a colloquial name or a more ...

I am working on a problem to distinguish between two binomial distributions. The resulting optimization problem is nonlinear and involves integer variables (number of binomial trials and number of ...

For instance, consider a module with the following general structure: ...

i'm looking for some advice for finite element analisys. i'm a biomedical engineering student with few knowledge about the FEM. Tools like Comsol and Ansys are very powerfull but also complex and i ...

I've professional experience with physics simulations and C++ programming, although I don't have specific experience with astrophysics simulations. I'm trying to build a two-body evolving system ...