All Questions

Suppose I know a function $f(t)$ and all its derivatives in $t$ in closed form. Given $a(0)$ and some $t_0>0$, I'm looking for an explicit integrator that can estimate $a(t_0)$, where $a(\cdot)$ ...

Briefly, Im currently solving chapter problems of Computational Fluid Dynamics Vol1 Hoffman K.A., Chang S. T. 2000 I can't find any solution guide or any source to verify my answers with. anyone can ...

We know in Strang splitting that the splitting error in the steady state solution is proportional to $h^2$. I want ask 2 things: If this error in the steady state solution is the global error? If we ...

We are currently in the process of implementing ports in our EM FEM simulation SW. We have come across the definition of boundary conditions for the ports, and we do not understand the equation for ...

Consider the problem $$ \left\{\begin{array} {rcl} -\Delta u & = 0 & \text{ in } \Omega \\ u & = 0 & \text{ on } \Gamma_D \\ \frac{\partial u}{\partial n} &= g &\text{ on } \...

Is there any estimate for the scaling of the number of function calls in BFGS-optimization with the dimensionality of the search space? Specifically I am assuming a (free) expression for the gradient ...

There is an area of thin mantle at the bottom of the ocean which is substantially raising the temperature of the sea bed due to a breach of molten material. In this assignment, you will use the heat ...

I'm modelling cracking of concrete structures. To do so I'm using interface elements [1-3]. In summary, these interface elements have a vanishingly thickness and are placed between two continuum ...

Are there iterative methods for the solution of nonsymmetric linear systems $Ax=b$ that can take (theoretical or practical) advantage from knowing that $A+A^T$ is positive definite? These matrices are ...

Can you please suggest a tool (software or online tool) that can analyze a submarine hull shape and give the total drag at a specific velocity. A simplified tool would work too, where I select a ...

I want an element as the one shown following. Nodes 6 and 8 are in the quarter position. Whether eight node quadrilateral element or six node triangle function can be used directly？ If not, how to ...

I'm studying the dealii tutorial number 4,5 and I understand the workflow. I've also been able to find the EOC by using manufactured solution where $f$ is a smooth r.h.s. and $\alpha(x)$ smooth too. ...

I'm looking for an algorithm for solving numerically, for u(t) and v(t), the following system: $$ u(t)=u_{0}-ct+\int_{0}^{t}\frac{a}{1+b_{1}e^{u(s)}+b_{2}e^{v(s)}}ds $$ $$ v(t)=v_{0}-Ct+\frac{CT}{\...

I have a scipy.sparse.linalg.LinearOperator object. I'd like to check if its associated matrix is symmetric without actually instantiating the matrix in the most ...

I am analyzing the stability of 1D convection (advection) equation as shown in the picture. When I derive the equations as shown I want to get rid of the complex number. I`m asking if those stability ...

Im trying to solve the Poisson equation in 1D: $$-u_{xx} = f(x), \hspace{6mm} u(a) = d1, \hspace{2mm} u(b) = d2$$Assuming a uniform partition such that $x_n = a + nh$, where $h = (b-a)/N$ and $n \in [...

Normally, this boards sees a lot of traffic about the most efficient and most powerful solvers for huge linear equation systems. But this time, I have the opposite problem: I need to implement a ...

In this article: https://www.geometrictools.com/Documentation/IntersectionOfCylinders.pdf the writer says: "If you plan on using cylinders for bounding volumes in a real-time graphics engine—...

I am trying to find the top k leading eigenvalues of a NumPy matrix (using python dot product notation) L@L + a*X@X.T, where $L$ ...

I'm new to matplotlib and trying to animate a 2D colormap to show diffusion in two dimensions. This is a method inside a class called Lattice2D with fields including lat_series (a numpy array of 2D ...

I try to use Fipy to solve the following 3 pdes system, I have implemented the above in python: ...

There are many rows of data in a database table, each of which contains many columns. ID (numeric - 12345, 12378, etc) Name 1 - AAA,BBB,CCC Name 2 - dd, ee, ff Name 3 - Ggg, Hhh, Iii The objective ...

I am playing with Galerkin Least-Squares stabilization to solve advection diffusion problem in the context of the finite element method. This works very well for steady-state advection-diffusion ...

Is there a generic algorithm to generate round-robin schedule with multiple teams on bye per round. For example I have N teams. Each team needs to play each other, but only M teams can play at each ...

I am working on 1-D mass transient diffusion in a radial domain (spherical object) using finite volume method. My equation reads $$\frac{\partial C}{\partial t} = D\left[\frac{\partial^2 C}{\partial r^...

I wrote a program which iteratively transforms data using matrix multiplications. To minimize the number of large memory allocations, I use two roughly equal-sized ...

I was looking for the fastest converging method to integrate a family of functions. After some tries, an old-school colleague suggested me a method that he used to use in excel to perform such task. ...

I need to integrate a function defined in 2Dims (z and radius r), for which I don't have an expression. I can just query the ...

Im working in comsol and needed help figuring out the objective function for the following situation (Comsol does have multiple objective function option as min max or sum of) I have 7 batteries ...

If $f(x)=\frac{\cos(x)-\cos(a)}{x-a}$, where $a$ is a fixed number, how to prove the following inequality \begin{equation} |f(x_1)-f(x_2)|\leq C|x_1-x_2|,\quad \forall~~ x_1,x_2\in \mathrm{R}.~~~~~~~~...

A spherical code, specified by the parameters $(n,N,t)$, is a set of $N$ coordinates on the $n$-dimensional unit hypersphere such that the set of dot products between any two unit vectors from the ...

I have written a Matlab code to solve the equation $-u'' = f$ with conditions $u(0) = u'(1) = 0$ on the domain $x \in [0,1]$. I tested the code with $f(x) = -2, \forall x\in [0,1]$. I check the plot ...

I am trying to get the structured mesh as shown in the figure. I have used the transfinite surface and curve to achieve the same. Though I get the structured mesh but I do not know how to do for body-...

I am trying to write an if statement that checks if 2 numbers are divisible before running some commands. The problem is, the rem function is giving some wrong results for certain number (2 is ...

Apologies if this is a trivial question. If that is the case I imagine I would benefit from someone explaining where my understanding is lacking. I am having some trouble interpreting the (putatively ...

Two random variables $X$ and $Y$ are distributed according to \begin{align} f_{XY}(x,y)= \begin{cases} x+y & 0\leq x \leq 1, 0\leq y \leq 1 \\ 0 & otherwise \end{cases} \end{align} I ...

I was reasoning about the behaviour of the methods I'm using for my simulation and I noticed that, considering $h_s$ as the timestep over which I have unstable solutions and $h_a$ as the timestep ...

I need to simulate a network of nodes. The weights of the edges are being given in a matrix . Due to the non-zero distances between the nodes, we consider time-delays, which are computed given the ...

I've seen two different optimizers being used, but both with a different solver. One uses PULP_CBC_CMD and the other uses ...

The idea of the method is to decompose the Navier-Stokes equation into the solenoidal and irrotational parts. $$\frac{\partial u}{\partial t}+u(\nabla \cdot u)=-\frac{1}{\rho}\nabla p+\nabla ^2 u$$ ...

I have the velocity (vector) and pressure (scalar). This solution is constant in each CELL (square) of the mesh. I don't know why does not appear the pressure information when I open the file in ...

I'm trying to plot the solution of a numerical method using a vtk file in paraview. The structure is very simple, and I going to explain with an example. I have a mesh of the unit square [0,1]x[0,1] ...

I am working on a non-linear least squares problem with standard form, in which I need to calibrate a parameter vector $\Theta$ to a set of inputs $\mathbf{x}$ and outputs $\mathbf{y}$: $$\begin{align}...

I have a system of non linear differential equations in the form : $$\frac{dy_i}{dt}=\sum_j a_{ij} y_i y_j $$. I first tried to solve it with Python suing ...

In the mathematical field of linear algebra and convex analysis, the numerical range or field of values of a complex $n\times n$ matrix $A$ is the set $$W(A)=\left\{{\frac {{\mathbf {x}}^{*}A{\...

I am interested in knowing some efficient techniques for solving the following extended Saddle point problem. \begin{align} \begin{bmatrix} A & B^T & C^T \\ B & 0 & 0 \\ C & ...

Briefly stated, I would like to find "all" local minima / critical points of a function. This function comes from the discretization of a continuous problem with infinitely many degrees of ...

Pseudospectra are typically computed by establishing a grid with $N$ points on a region of the complex plane, computing the resolvent norm $||(zI − A)^{−1}||$ at each grid point z, and visualizing ...

I am writing a project about the Finite element method for use in high-frequency solutions of Maxwell's equations. This could be for use in antenna design and similar. I have some trouble ...

I am trying to solve the ODE : $\frac{d^2T}{dx^2} = \omega_1 T+\omega_2 T^2$ + using different numerical methods. I have tried the following discretizations so far and none of them seem to be grid ...