All Questions

So, my question is if one should ideally keep a record of all seeds that are used when publishing numerical work that involves one or more random number generators (e.g. a stochastic simulation), and ...

I have implemented finite-difference WENO scheme for Euler equations (with some variants - WENO-JS, WENO-Z, WENO-M, different flux splitting). It works well, but have problem with so-called carbuncles ...

Ridge regression can be posed as minimizing the following objective function (over $x$): $$\frac{1}{2} \lVert Ax - b \lVert_2^2 ~+ \frac{\lambda}{2} \lVert x \lVert_2^2 $$ Which has a closed form ...

I have a matrix $A \in \mathbb{R}^{m \times n}$ where $m \gg n$ and I want to compute the full QR decomposition $A = QR$. Where $Q$ is an orthogonal $m \times m$ matrix. Bishof & Van Loan (1987) ...

Is the change in time step necessary for the grid independent study? As the CFL is based on the relation between dt and dx. In mesh independent study, only change should be mesh i.e, dx isn't it so?

I need to take integer square roots $\lfloor \sqrt{n}\rfloor$ of (lots of) 128 bit numbers $n$. Calling gmp seems to take surprisingly long (though I can't tell for sure, since gmp routines are not ...

Help me understand a part of Brent's root finding algorithm. In a typical iteration we have samples (a,fa), (b,fb), (c,fc) all real with (a<b<c) or (c<b<a) . Also, in the case I am ...

I'm trying to solve a Schrodinger equation of the form $i\frac{\partial}{\partial t}\psi=-\frac{\partial^2}{\partial x^2}\psi + (V(x)+\alpha|\psi|^2)\psi$ using the split-step Fourier method ...

I am currently using Task Spooler, which is a job scheduler I have installed on my iMac. I have encountered a problem in which I cannot execute a job properly. Using a bash script, this is how I run ...

I am trying to solve a 2D dynamic linear elasticity model parallel in time using Xbraid. The spatial domain is [0,1]x[0,1] and time domain [0,1]. For time integration I am using a backward Euler ...

I am looking for a concise description to help me understand the error for Monte Carlo Integration using Uniform Sampling and Importance Sampling For Importance Sampling I have that the error is just ...

I currently have a code that solves $u_t+ cu_x=0$ with periodic boundary conditions, and constant $c$ (using an upwind method). I'm wondering how I would alter this code to solve something of the form ...

Starting from $$ c_p \frac{\partial u }{\partial t} = k \nabla^2 u $$ in a one dimensional domain [0,1] where $c_p$ and $k$ are modeling two different materials: $$ k = \begin{cases} 1 ~\text{if} ~x &...

I am trying to build a triangle mesh of the surface of a sphere which also includes a subdomain defined by a 'polygon'. Here is a successful example (subdomain defined by the red dots): Note that the ...

I am trying to solve the Poisson Equation $\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 32(x(x-1) + y(y-1))$ for a 61x61 grid using Python3 with boundary conditions being $T=...

I am trying to implement 3D tetrahedral elements in my finite element code (which works fine for linear triangles and quadrangles in 2D). But my simulations are crashing with tetrahedral elements. My ...

I have a linear system of the form $A x = b$ where $A$ and $b$ are known, $A$ is "square", and $\lvert b \rvert_1 = \lvert x \rvert_1 = 1$. Unfortunately, I am working in a framework that ...

Consider independent random variates $X_0, X_1, . . .$ each uniformly distributed on the support $[0, 1)$ Let's say $Y = X_0 + X_1$, where $X_0$ and $X_1$ are independent uniform random variables with ...

I'm making a NVT Monte Carlo (MC) simulation code with only short range interaction. I found many MC tutorial codes (usually Lennard-Jones system) in online. However, most of them are doing energy ...

I'm working on a 2D model to simulate groundwater flow through pores using the Darcy's law interface. I'd like to eventually tie in flow and transport of diluted species. The domain is defined as a 0....

I am doing a solar-system simulation. I am using Ruth's 3rd order sympletic integrator to avoid the problem of Energy Drift (which I had with RK4), but the the planets quickly leave orbit, and energy ...

I am trying to embed an animation using FuncAnimation from matplotlib into a tkninter GUI. In the execute button at the bottom I am calling the Execute function. If I click the execute button many ...

I am trying to solve the linear finite element equation $M\ddot{u}+Ku=F(t)$, where $M$ is the mass matrix ,$K$ the stiffness matrix and $F(t)$ the external load vector, parallel in time using XBraid ...

In particular, I want to focus on finding the volume $V$ because I will need it to start working on solving the centre of mass This $3D$ homogenous body (Torus section) is defined by $$x^2 + \left(\...

I am implementing an adaptive 3D FMM with the "basic" $O(p^4)$ translation operators. I am looking for clarification on the multipole-to-multipole (M2M) translation operator. I will explain my ...

Update (Solution) -17 October 2020- I finally did it! You can check the code on my GitLab repo. The function is to do this is the domain_extract which identifies ...

I would like to solve two types of simple 2D problems, namely the stationary heat equation on an L shaped geometry like this: And also compute the magnetostactic field in an air gap of the following ...

I want toconstruct a difference method for the the numerical approximation of the solution of the following boundary value problem: $u:[a,b]\to \mathbb{R}$ function,such that $$ -u''(x)=f(x)$$ and $u(...

I have a very basic notion about interval arithmetic (IA), but it seems to be a very interesting branch of computational science both theoretically and practically. It is clear that the obvious ...

How to best export Scene/Screenshot in Paraview as a vector graphic? It seems PDF and PS export are not working really good for me (Paraview 5.3/5.5/5.8), either the scene is cropped at the borders or ...

I hope that one of you guys can help me because i have been stuck here for a week. I am trying to read a gmsh file (.msh) using dolfin convert to XML and then download it with dolfin. The thing is ...

Initially I thought that this is the kind of question which ought to have already been answered in the form of an example online, but so far I haven't found one. I will admit that I am very new to ...

I am looking for the details of commonly-used predictors for accelerating the convergence of iterations using Newton-Raphson scheme for nonlinear problems in FEM. I am looking specifically for static ...

I am looking for a simple to implement algorithm for the bipartite euclidean matching problem (or an implementation of any practical algorithm). I am aware of Agarwal's paper, but I would like to ...

I am trying out odeint and received the error 'Excess work done on this call (perhaps wrong Dfun type).'. The values returned are also super sensitive to small ...

what is the time complexity of gradient $\nabla_{f}$ using the $\mathcal O$-notation? what is the time complexity of jacobian matrix using the $\mathcal O$-notation? who knows some references to ...

I have a function $f:\mathbb R^N\to \mathbb R$ and I would like to compute all the partial derivatives of $f$ w.r.t. the $N$ input. What is the computational complexity using the (ones-sided) finite ...

I want to solve a linear set of equations (Ax=b) using LU decomposition. My "A" matrix is a complex matrix which is ...

Using Sympy, I would like to compute the negative binomial expansion of a general symbolic polynomial, e.g., $(x_1 + x_2 + x_3 + 4 x_4)^{-1}$. I understand that I can go by recursively partitioning ...

Let $A$ be a matrix with real entries, and let $A_+$ be $A$ augmented by a single column. From linear algebra we know \begin{equation} \operatorname{rank}(A_+) = \operatorname{rank}(A) \hspace{10pt} ...

When I use the newton's method or hybrid solver in the GSL package to deal with 1-D or multidimensional root solving problems, the code frequently crashes when the solver requests function value ...

This is my first time asking a question here, so I may not be asking this in the right place. I am trying to find the roots of a monotonic function with as few function evaluations as possible. I ...

I am reading a book on digital circuits. It says that given a n-bit binary number $N$, its two's complement representation is itself, if $N$ is positive; and its two's complement representation is $2^...

I need to optimize a code where the most performance critical part is doing a 'change of basis', in other words it is an unitary similarity transformation on a big real positive definite symmetric ...

In many modern papers Navier-Stokes equations are solved with finite-difference or finite-volume methods using WENO reconstruction for non-viscous fluxes and central differences for viscous ones. It ...

In my application, I have two general real matrices $A$,$B$ defined as follows, $$ A=\begin{bmatrix} -s I_3 & A_0 & 0 & 0 \\ A_0^T & -s I_3 & 0 & 0 \\ 0 &...

I need to slove one optimization problem of quadratic programming. The number of optimization variables is about 16,000. The constraints include equality constraints and inequality constraints. I have ...

I have implemented a constitutive equation of elastic materials (Hooke's law) in my 3D weakly compressible SPH solver based on [1]. The coding seems to be correct. To verify the implementation I ...

Most of the time, when I see someone reporting the average timing of a certain algorithm on a computer in a computational mathematics paper, they do something like this: Run the operation $n$ times (...

I am trying to solve $M\ddot{u}=-Ku+F_\text{ext}$ for a 2D linear elastic model with $M$ be the mass matrix,$K$ the stiffness matrix and $F_\text{ext}$ the external load vector coming from a uniformly ...