# All Questions

7,599 questions
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) ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
74 views

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)=... 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 ... 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? 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 ... 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)... 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 ... 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 ... 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 ... 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: ... 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 ... 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 ... 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-... 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(... 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/... 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? 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) = 1for (x, y)\in [0, 1]\times [0, 1] with ... 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 ... 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) ... 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? 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 ... 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 ... 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 ... 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: ... 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 ... 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}$$The ... 0answers 17 views ### Non linear Parametric BVP with inequalities Consider a non linear ode in dimension 10: \dot x = f(t,x,\lambda) where \lambda is a vector of p parameters. Consider a boundary value problem of the form : \dot x(t) = f(t,x(t),\lambda) ... 1answer 60 views ### Dirichlet boundary conditions in generalized eigenvalue problem Let us consider a problem of the form$$(\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} ... 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 $$E(\{\widetilde{C_{i}}\}) = \sum_{i}\left[ \left( 1-\psi _{i}\right) \left\| \widetilde{C_{i}}-\sum_{j\in{N_{i}... 1answer 47 views ### Adam Bashforth 4 method: how to determine starting values and stil keep the the order of accuracy I am using an Adam Bashforth 4 method to solve an IVP problem so I need other numerical method to estimate the first 3 values. I am very much interested in finding a way to estimate the first 3 values ... 0answers 43 views ### Reduced row echelon form of a rectangular sparse matrix I am trying to find the reduced row echelon form of (m x n, m >= n or m <= n) a rectangular sparse matrix (CSR format) to possibly deal with millions rows and columns which causes memory allocation ... 0answers 96 views ### Finite Difference Solver Heat Equation I am trying to write a finite difference solver for the heat equation in Python using FTCS implicit scheme. My details are below; \frac{\partial{T}}{\partial{t}} = \frac{\partial^2{T}}{\partial{z}^2}... 0answers 30 views ### Finding the Proportions of and Programatically Representing Topological Disks I am currently in the process of writing an internal software package that will be used for computational geometry research. I am interested in being able to programatically generate isotoxal ... 0answers 43 views ### How to solve coupled equations in python I'm having serious troubles with translating 3 coupled differential equations into python. The 3 DE's stem from a 4th order DE used to calculate the bending moment of an underwater pipeline that has ... 1answer 47 views ### Combining multiple coupled 1st order equations in python I'm having serious troubles with solving translating 3 coupled differential equations into python. The 3 DE's stem from a 4th order DE used to calculate the bending moment of an underwater pipeline ... 1answer 49 views ### Imposing zero mean condition in FEM I wanted to solve a periodic elliptic equation of the form$$-\nabla\cdot(A\nabla u)=-\nabla\cdot F$$on Y=[0,2\pi)^d using FreeFem++, where A and F are Y-periodic. The space of solutions is ... 0answers 25 views ### Determine endpoint of a graph given as a list of nodes + direct successors and predecessors [migrated] I fix a type T once for all. (Concretely, T is a c# class, but that doesn't matter.) On T I have the notion of direct successor ... 0answers 16 views ### How to distinguish different cracks/enriched regions in Abaqus from UDMGINI subroutine? I want to use different failure criteria for two or more separate enriched regions in one model. The regions are always in different instances made from different materials. I've tried to get ... 1answer 16 views ### Minimize squared error of linear function Let M be a m \times n matrix, x a n-vector, y a m-vector, and \|\cdot\|_2 represent the L_2 norm (i.e., Euclidean norm). Given M,y, the goal is to find x that minimizes the ... 0answers 27 views ### Minimizing the ratio of two specific non negative quadratic convex functions F is m\times m diagonal, with real non negative elements D is n \times m complex P is n \times 1 complex A is m \times 1 complex. Minimize \Gamma(A), with respect to A.$$\... 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"? 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. 2answers 67 views ### projective reconstruction from orthogonal views This is a problem from projective geometry. Suppose I have a vectorz \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 ... 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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