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30 views

Numerical integrator for $a'(t)=e^{-a(t)}f(t)$

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 $a(\cdot)$ ...
-2
votes
0answers
24 views

hoffmann cfd solutions

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 ...
2
votes
0answers
40 views

How does the error work for the Strang Splitting?

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 ...
0
votes
0answers
39 views

FEM port Boundary definition for electromagnetics and wave guides

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 ...
2
votes
0answers
32 views

A priori error estimates - finite element method - mixed boundary conditions

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 } \...
4
votes
1answer
85 views

How does the number of function calls in BFGS scale with the dimensionality of space

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 ...
-2
votes
0answers
22 views

solving heat equation using analytic and numeric solution [closed]

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 ...
0
votes
0answers
44 views

(FEM) Solving ill-conditioned linear system due to small elements

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 ...
6
votes
0answers
71 views

solving linear system whose symmetrized matrix is positive definite

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 ...
0
votes
0answers
64 views

Tool that calculates total drag for a submarine

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 ...
1
vote
1answer
63 views

Shape function for quarter point element from degenerate quadrilateral

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 ...
1
vote
2answers
123 views

Manufactured solution for $-\operatorname{div}(a(x) \nabla{u}) = f$ when $\alpha(x)$ is discontinuous

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. ...
-2
votes
0answers
32 views

How to solve numerically the following non-linear mixed Volterra-Fredholm integral equations system?

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}{\...
3
votes
0answers
48 views

Check if LinearOperator is symmetric

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 ...
1
vote
0answers
47 views

Stability plot of upward difference implicit time

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 ...
1
vote
1answer
38 views

Finite Element Method for 1D Poisson Equation with Inhomogeneous Boundary Conditions

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 [...
0
votes
2answers
78 views

Simplest solver for linear equation systems

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 ...
2
votes
0answers
40 views
+50

Why is bounding a surface with a capsule is better than with a cylinder to detect intersections?

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—...
3
votes
1answer
72 views

Lanczos algorithm for finding top eigenvalues of a matrix sum

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 $L$ ...
0
votes
0answers
15 views

Animating a 2D colormap from existing array using matplotlib [migrated]

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 ...
-1
votes
0answers
26 views

Using fipy solving pde system [closed]

I try to use Fipy to solve the following 3 pdes system, I have implemented the above in python: ...
0
votes
0answers
21 views

I need help developing a process to map many individual records (from a database) into larger groups

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 ...
3
votes
0answers
70 views

Galerkin Least-Squares stabilization for FEM solution advection (hyperbolic) equations

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 ...
0
votes
0answers
13 views

Generate round-robin schedule with multiple byes [closed]

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 ...
0
votes
0answers
37 views

The physical meaning of conservative mass in diffusion equation

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^...
1
vote
0answers
42 views

Why does Eigen allocate a temporary to evaluate A.noalias() = B.transpose()*C in parallel?

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 ...
5
votes
0answers
116 views

Why does this integral converge faster than normal rectangle or trapz integration?

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. ...
0
votes
0answers
22 views

How to efficiently perform this 2D integral in Quadpy?

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 ...
0
votes
0answers
39 views

Help with finding an objective function for optimization

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 ...
0
votes
0answers
62 views

How to prove the Lipschitz continuity of the following functions? [migrated]

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}.~~~~~~~~...
3
votes
3answers
120 views

Algorithms to generate spherical codes

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 ...
0
votes
0answers
68 views

Error $L_{2}$ convergence in Finite Element for Poisson Equation

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 ...
-1
votes
1answer
35 views

Generating structured paraboloid using gmsh

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-...
0
votes
1answer
33 views

Rem function in Octave showing wrong result

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 ...
0
votes
2answers
81 views

Validating that a code is a good spherical code

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 ...
-1
votes
1answer
36 views

Generating Rvs for a given PDf in python

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 ...
1
vote
1answer
91 views

Accuracy gap for apparently stable solution

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 ...
-1
votes
1answer
44 views

How to reduce computational time in DDE simulation on Matlab

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 ...
1
vote
1answer
30 views

Difference between LP optimization and GLPK optimization

I've seen two different optimizers being used, but both with a different solver. One uses PULP_CBC_CMD and the other uses ...
4
votes
1answer
104 views

Projection method FVM poisson part, adding source term

The idea of the method is to decompose the Navier-Stokes equation into the solenoidal and irrotational parts. $$\frac{\partial u}{\partial t}+u(\nabla \cdot u)=-\frac{1}{\rho}\nabla p+\nabla ^2 u$$ ...
0
votes
0answers
13 views

Plot scalar and vectorial solution constant on each CELL=square in paraview/vtk

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 ...
0
votes
0answers
9 views

Plot a function (constant on each square=CELL) in paraview using vtk file

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] ...
0
votes
0answers
35 views

Blown-up iterates in Gauss-Newton method

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}...
2
votes
0answers
86 views

Find time step for Euler method in numerical solving of a system of non linear differential equations

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 ...
1
vote
0answers
74 views

Numerical Range of a matrix in Python

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{\...
3
votes
2answers
93 views

Efficient schemes for solving the extended Saddle point problem

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 & ...
5
votes
0answers
82 views

How to find a lot of (if not all) local minima / critical points of a function?

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 ...
0
votes
1answer
32 views

Pseudospectra in R implementation

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 ...
3
votes
1answer
111 views

Finite element method for high-frequency electromagnetics

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 ...
0
votes
1answer
97 views

Discretization of a non-linear ODE using FDM isn't grid indepenent

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 ...

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