# All Questions

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### Guidelines for publishing data from a stochastic simulation

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 ...
180 views

### Is there a simple way to avoid carbuncles for FD WENO methods?

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 ...
606 views

### Clever ways to update LU factorization for ridge regression

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 ...
49 views

### “WY” representation of QR factorization — implementations?

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) ...
38 views

### Grid Independence Study

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?
36 views

### Hack for using hardware to take square roots of 128 bit numbers

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 ...
48 views

### Help understanding Brent's root finding method

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 ...
648 views

### Split-step Fourier method applied on Schrodinger equation

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 ...
22 views

### Task Spooler – Executing an Executable within an Executable

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 ...
20 views

### Multigrid Reduction In Time Convergence

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 ...
15 views

### Error in Monte Carlo integration

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 ...
24 views

### discretizing advection equation with variable wave speed + stability

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 ...
133 views

45 views

### Clarification regarding 3D FMM translation operators

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 ...
46 views

### Determining the voxels between two boundary surfaces

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 ...
99 views

### (Lack of) Availability of Finite-Difference library for simple 2D PDEs

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 ...
35 views

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### Efficient change of basis real positive definite symmetric matrix

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 ...
41 views

### Haw to apply central difference to viscous flux in energy equation?

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 ...
121 views

### A misunderstanding or a bug in LAPACK's solver for generalized eigenvalue problems?

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 &...
27 views

### Implementation method selection for sparse constrained linear least squares or quadratic programming

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 ...
146 views

### How to make objective elastic SPH model?

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 ...