All Questions

5
votes
3answers
204 views

Fast evaluation functions given by straight-line programs

I have a simple but long function that takes a vector x[10], and outputs a vector y[100]. It is an automatically generated eval function for a multivariate polynomial, ie, there is only (complex) ...
0
votes
1answer
34 views

How do I get power from gaussian beam numerically?

I would like to get the power from a Gaussian beam given a set of points at which electric field is evaluated. Please follow my reasoning and tell me what assumption maybe are wrong Power definition ...
1
vote
3answers
115 views

Find a solution of large system of inequalities

I have a large system of homogenous inequalities involving 33 real unknowns of the form $$ \vec{F}(z_i)^T \cdot \vec{X}>0\, $$ where $\vec{X} = \left(x_1,...,x_{24}\right)^T$ are the unknowns and ...
0
votes
0answers
9 views

What to call an analogous limiting reagent?

I'm trying to find either an Excel function or some other calculator that will tell me the number of possible complete combinations/sets of an item given amounts of components. I'm a high school ...
2
votes
1answer
52 views

Parallelizing FEM for elliptical PDEs with n >1

For a little personal project, I am picking up my FEM skills again. I learned a lot about the theory back in university and I am able to implement a simple FEM solver for specific problems but I was ...
0
votes
0answers
21 views

Roller boundary conditions in a 4 or 3 point bend test

I came across this post Boundary conditions in a four point bend test I don't have the reputation count to comment, so I'm making a follow-up post. I am curious about @Bill Greene's comment under ...
2
votes
0answers
42 views

Non-parametric models as solutions to Partial Differential Equations

In the realm of scientific computing, there are a plethora of techniques developed to solve Partial Differential Equations (PDEs). Many of the popular methods are variants of common techniques such as ...
0
votes
1answer
74 views

Actual global error vs theoretical global error: How to combine theory with practice

I have implemented an Adams Bashforth 4 method to solve an Initial Value Problem for an ODE and I am testing it against the test equation: $y'=\lambda y$ with $y(0)=1$ with the exact solution: $y(t)=...
3
votes
0answers
26 views

Detecting blocks in non-linear system of equations

When solving systems of non-linear equations using Newton's method, it is often observed that the system has an independent sub-system, e.g. : $$ f(x,y) = 0 $$ $$ g(x,y) = 0 $$ $$ h(x,y,z) = 0 $$ If ...
5
votes
3answers
171 views

Why is the FVM traditionally used in CFD, and FEM in computational structures?

Most CFD codes use FVM. Most computational structures codes use FEM. Why is the FEM not frequently used in CFD, and why is FVM not frequently used in FEM?
4
votes
1answer
59 views

What is the name for this type of constraint?

I have what would be a straightforward mixed-integer linear programming problem, except for the fact that some of the constraints are of the form $f(x_1,x_2,x_3,\ldots,x_n) < c$, where $f$ is 'take ...
3
votes
2answers
104 views

Finite volume discretization of non-conservative linear hyperbolic equation

Problem. Consider the one-dimensional adjoint Euler equations for $(x,t) \in \Omega \times [0,T]$ with $\Omega \subset \mathbb{R}$ and $T > 0$ $$ \varphi_t + \Big(\frac{\mathrm{d}F}{\mathrm{d} U}(x)...
0
votes
1answer
56 views

Structural boundary conditions - rotational/translational DoFs and displacement/tractions BCs

I am a little bit confused over the concept of translational and rotational degrees of freedom (DoFs) in structures, and their relation to displacement/traction BCs. Do displacement boundary ...
1
vote
0answers
51 views

Finite element method for Surface integrals using polar coordinates

I am trying to solve a 2D elliptic PDE (see complete electrode model for electrical impedance tomography) using the finite element method (FEM) over a circular region $\Omega$. I have discretized the ...
1
vote
0answers
22 views

Boundary Conditions involving exponential functions of nodal unknowns

I am fairly new to Computational Engineering and I have mainly been exposed to using the Finite Difference Method to produce Linear Systems and solve them using Iterative Methods. I am trying to ...
1
vote
1answer
58 views

Area and volume of P2 elements

Context: For a fluid solver, I need to compute areas and volumes of curved elements. My curved elements are quadratic triangles and quadratic tetrahedra, defined by their Lagrange nodes. Question: ...
9
votes
3answers
298 views

fastest linear system solve for small square matrices (10x10)

I am very interested in optimizing the hell out of linear system solving for small matrices (10x10), sometimes called tiny matrices. Is there a ready solution for this? The matrix can be assumed ...
-1
votes
0answers
41 views

Numerical solution to a set of equations

I'm doing an extracurricular exercise to have an easier examn on my mathematics course. The teacher told me to solve numerically a set of equations, in particular: And the teacher told me that in ...
0
votes
0answers
12 views

Cost functions to judge time/memory/accuracy tradeoffs

I am working on an interesting algorithm: Its absolute error is exponential in a parameter $j \in \mathbb{N}$, and for a given $j$, I have complete freedom to choose between an $\mathcal{O}(1)$ time-...
0
votes
0answers
26 views

correct way to implement a 3/8ths-rule RK4 solver for a changing wind field

I am trying to simulate particles in a wind field. The wind field is variable and changes over both position and time. I can sample the wind vector at a given position p and a given time t using wind(...
2
votes
0answers
46 views

Structural Analysis Library

Can anyone recommend a structural analysis library that satisfies the following requirements: C++ API Simulate both beam elements and shell (slab) elements Both static and dynamic analysis Free and/...
2
votes
1answer
63 views

public solvers for the time-dependent Schrödinger equation?

Are there efficient public solvers for the time-dependent Schrödinger equation with time-independent Hamiltonian and 2 or 3 degrees of freedom?
0
votes
0answers
29 views

Numerically solving the poisson equation, discretisation of the differential operator, mistake?

I'm attempting to numerically solve the poisson equation using Numpy's LinearOperator class. $$-\nabla \cdot \left(\sigma(x, y)\nabla\right)u(x, y) = 1$$ for $(x, y)\in [0, 1]\times [0, 1]$ with ...
0
votes
0answers
35 views

Representatoins in floating point arithmetic

I read 'Pivoting for LU Factorization'. On page 3, I found something incomprehensible: When these computations are performed in floating point arithmetic, the number $2−10^{-20}$ is not represented ...
1
vote
1answer
49 views

Mixed formulation in 1D

I have been working on a hybrid dimensional model using the mixed FEM formulation, in which 3D elements and 2D elements are combined by certain relationships between the degrees of freedom (DOFs) ...
0
votes
0answers
25 views

Cardinal B-Splines with derivative information

Have Schoenberg's cardinal B-splines been extended to accept derivative information at each knot, similar to how Lagrange interpolation can be improved by Hermite interpolation?
0
votes
1answer
51 views

Ordering points from X Y coordinates

I have series of points extracted from a regular grid, with their X/Y coordinates. A previous algorithm (that I cannot modified!) output a list of these coordinates, but the ordering of these point is ...
0
votes
0answers
38 views

Strange behavior in multi-layer orthotropic material subject to 4 point bending

I am modeling a beam subject to a 4 point bend using a linear elastic solver. The beam has 3 layers of different orthotropic materials, layered in the thickness direction. The load is applied in the ...
2
votes
1answer
121 views

Mass Matrix and how to handle it (ODEs) - References

I'm interested in a good reference/paper about how to handle numerically a mass-matrix system as \begin{align} \mathbf{M}(t,y)\dot{y} =F(y,t) \end{align} I know that such a problem can be solved by ...
0
votes
0answers
28 views

How to set delta function boundary condition in FEniCS?

For a unit square, I'd like to choose points on its boundary where the desired solution takes the value 1, and at all the other boundary points it is 0. I tried to implement this in the following way: ...
6
votes
2answers
73 views

Algebraic multigrid for complex valued matrices

Assume one uses the classical AMG with Ruge-Stuben coarsening and direct interpolation for solving real valued problems. How can this approach be recycled to also solve complex valued problems like ...
0
votes
0answers
32 views

Discrete maximum principle for discretized ODE

I discretized the following ODE using central finite differences for 1st and 2nd derivatives: $$u''-bu'=f(u), x\in (0,1)\\u(0)=1, u'(1)=0\\ b>0, f:\mathbb{R_{\ge 0}}\to \mathbb{R}_{\ge 0}$$ The ...
0
votes
0answers
17 views

Non linear Parametric BVP with inequalities

Consider a non linear ode in dimension $10$: $\dot x = f(t,x,\lambda)$ where $\lambda$ is a vector of $p$ parameters. Consider a boundary value problem of the form : $\dot x(t) = f(t,x(t),\lambda)$ ...
5
votes
1answer
60 views

Dirichlet boundary conditions in generalized eigenvalue problem

Let us consider a problem of the form $$(\mathcal{L} + k^2) u(\mathbf{x})=0\, ,\quad \forall \mathbf{x} \in \Omega$$ with Dirichlet boundary conditions $$u(\mathbf{x}) = 0, \quad \forall \mathbf{x} ...
0
votes
0answers
90 views

How to solve extremely large scale linear system

I have a extremely large scale liner system equation. It stems from the minimization of $$ E(\{\widetilde{C_{i}}\}) = \sum_{i}\left[ \left( 1-\psi _{i}\right) \left\| \widetilde{C_{i}}-\sum_{j\in{N_{i}...
0
votes
1answer
47 views

Adam Bashforth 4 method: how to determine starting values and stil keep the the order of accuracy

I am using an Adam Bashforth 4 method to solve an IVP problem so I need other numerical method to estimate the first 3 values. I am very much interested in finding a way to estimate the first 3 values ...
0
votes
0answers
43 views

Reduced row echelon form of a rectangular sparse matrix

I am trying to find the reduced row echelon form of (m x n, m >= n or m <= n) a rectangular sparse matrix (CSR format) to possibly deal with millions rows and columns which causes memory allocation ...
-2
votes
0answers
96 views

Finite Difference Solver Heat Equation

I am trying to write a finite difference solver for the heat equation in Python using FTCS implicit scheme. My details are below; $\frac{\partial{T}}{\partial{t}} = \frac{\partial^2{T}}{\partial{z}^2}...
-1
votes
0answers
30 views

Finding the Proportions of and Programatically Representing Topological Disks

I am currently in the process of writing an internal software package that will be used for computational geometry research. I am interested in being able to programatically generate isotoxal ...
-1
votes
0answers
43 views

How to solve coupled equations in python

I'm having serious troubles with translating 3 coupled differential equations into python. The 3 DE's stem from a 4th order DE used to calculate the bending moment of an underwater pipeline that has ...
0
votes
1answer
47 views

Combining multiple coupled 1st order equations in python

I'm having serious troubles with solving translating 3 coupled differential equations into python. The 3 DE's stem from a 4th order DE used to calculate the bending moment of an underwater pipeline ...
0
votes
1answer
49 views

Imposing zero mean condition in FEM

I wanted to solve a periodic elliptic equation of the form $$-\nabla\cdot(A\nabla u)=-\nabla\cdot F$$ on $Y=[0,2\pi)^d$ using FreeFem++, where $A$ and $F$ are $Y$-periodic. The space of solutions is $...
0
votes
0answers
25 views

Determine endpoint of a graph given as a list of nodes + direct successors and predecessors [migrated]

I fix a type T once for all. (Concretely, T is a c# class, but that doesn't matter.) On T I have the notion of direct successor ...
-1
votes
0answers
16 views

How to distinguish different cracks/enriched regions in Abaqus from UDMGINI subroutine?

I want to use different failure criteria for two or more separate enriched regions in one model. The regions are always in different instances made from different materials. I've tried to get ...
0
votes
1answer
16 views

Minimize squared error of linear function

Let $M$ be a $m \times n$ matrix, $x$ a $n$-vector, $y$ a $m$-vector, and $\|\cdot\|_2$ represent the $L_2$ norm (i.e., Euclidean norm). Given $M,y$, the goal is to find $x$ that minimizes the ...
0
votes
0answers
27 views

Minimizing the ratio of two specific non negative quadratic convex functions

$F$ is $m\times m$ diagonal, with real non negative elements $D$ is $n \times m$ complex $P$ is $n \times 1$ complex $A$ is $m \times 1$ complex. Minimize $\Gamma(A)$, with respect to $A$. $$\...
1
vote
1answer
109 views

Do there exist “frameworks” as to how computational scientific experiments claim validity? Scientific method for computed science?

Do there exist "frameworks" as to how computational scientific experiments claim validity? Like "scientific method for computed science"?
-1
votes
0answers
22 views

implementing custom force laws in OpenFOAM

How can I implement a custom force law (e.g., Van der Waals's forces) in OpenFOAM? I am new to OpenFOAM.
2
votes
2answers
67 views

projective reconstruction from orthogonal views

This is a problem from projective geometry. Suppose I have a vector $z \in R^k$ of unit length $\| z \| =1$ inside a $k$-dimensional hypercube. I don't know its value but do know its projection upto ...
1
vote
0answers
63 views

PDE discretization on triangular domain

Given the 2D Poisson equation $$\Delta u = f\\ u(x,0) = g_1(x), 0<x<1\\u(0,y) = g_2(y), 0<y<1\\ \partial_n u (x, 1-x) =0, 0<x<1$$ defined on the domain $\Omega := \{(x,y) \in \...

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