All Questions

Pasted below is my python code. It is a 4th order runge kutta that evaluates the 2nd order ode: y'' +4y'+2y=0 with initial conditions y(0)=1, y'(0)=3. I need help fixing it. When I run my code, my ...

I have a cell centered cartesian grid and am trying to implement the flux inside the divergence term using numerical flux with a flux limiter. I found different formulas for MUSCL flux limiter, where ...

I am taking a computational linear algebra course and i got stuck during a homework problem concerning the computation of inner products. I am supposed to compute the inner product:$$\mathrm{a}_{\...

I have some data that looks like as follows x-cor y-cor z-cor 0.02 0.0251 0.02 0.01 0.0257 0.02 0.014 0.02 0.03 0.023 0.003 0.05 0.013 0.002 0.77 .................... .................... ...

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 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 ...

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) ...

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 ...

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 ...

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 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 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 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 ...

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 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 ...

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 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 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 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 ...

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 ...

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 ...

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 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 ...

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 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 ...

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 ...

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

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^...

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 ...

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 ...

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 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 ...

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} ...

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 a linear elasticity model using finite element discretization in a rectangle domain [0,1]x[0,1]. For the solution of the the linear system $Ku=F$ I am using the CG algorithm. ...

I have an interesting little problem that I believe can be formulated in terms of optimization or constraint programming. I have a few dozen variables $a$, $b$, $c$ ... and a set of constraints that ...

One of the most challenges in distributed consensus mechanisms is both time complexity and message complexity. For example, PBFT message complexity is O(n^2) that ...

Consider a nonlinear hyperbolic conservation equation: $$ \partial_{t}u = -\partial_{x}f(u) $$ The spatial derivative of $f(u)$ may approximated after a spatial discretization by $x_{j}=j\Delta x$ $$ \...

In Computer Systems: a Programmer's Perspective: Writing TMin in C In Figure 2.19 and in Problem 2.21, we carefully wrote the value of TMin32 as -2,147,483,647-1. Why not simply write it as either -2,...

From Computer Systems: a Programmer's Perspective: With single-precision floating point the expression (3.14+1e10)-1e10 evaluates to 0.0: the value 3.14 is lost ...

I have two data vectors $y1$ and $y2$, and I want to plot both of them as functions of the vector $x$. I want the result to be two overlapping curves. Here is the set of commands I am using. y2=[0.003,...

When one equality-constrained optimization is formulated, the method of Lagrange multiplier will be the choice for me. In Chapter 17 from the book Numerical Optimization, quadratic penalty method can ...

I am trying to get the numerical integration of a function using scipy's integrate.quad as follows. $$ \begin{equation} G (\alpha) = \frac{4\alpha}{\pi}\int_0^{\...

I actually have this data locality as a possible problem for why my fortran program runs somewhat slow. In one part of this program, I have nested loops and throughout these loops, a given section of ...

I have the following problem: $$\min_{x\in \mathbb{R}^n}\|Ax-b\|_1$$ where the matrix $A$ is large and sparse. I am looking for methods/code that can minimize this efficiently. References are very ...