# All Questions

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### Finding the polynomial for the solution of an ODE

I’m stuck trying to solve part (b) and (c) of the below problem, but part (b) is the one of main concern here as I think (c) should follow easily once (b) is completed. I don’t know where to start ...
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### Finite dimensional optimization problem over dynamical system

I am interested in solving numerically the following mathematical problem Consider an ode of the form $$\dot q(t) = f(q(t),t_1,\ldots, t_N),\qquad t\in [0,T],$$ where $q\in \mathbb{R}^n$ is the ...
107 views

### Is there any explicit symplectic Runge-Kutta method?

As far as I know, all the symplectic Runge-Kutta methods are implicit which need to solve non-linear equations during the calculation. Is there any explicit method? If not, why?
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### How to efficiently invert $K \otimes M+I_T\otimes \Sigma$?

I'm looking for a way to efficiently invert $$K \otimes M+I_T\otimes \Sigma$$ where the inverses for $M,K$ exist. $I_T$ is the identity matrix of dimension $T$, and $\Sigma$ is a diagonal matrix, with ...
73 views

### Automatic differentiation via ADOL-C and the Heaviside Function

I am writting a c++ program in which I define a function $$\displaystyle F(t) = \sum_{i}r_i\,H(t-t_i)$$ where $H$ is the heaviside function, $t_i$ are optimal parameters which are mutable. The ...
49 views

### Strange spectral (finite) element results of a solid plate

I tried to implement the spectral element method1 as proposed in . I simulated an aluminum plate and a vertical concentrated force was applied at the middle of the top left quarter of the plate2. I ...
93 views

### How to solve a 4th order nonnegative LASSO problem?

I need to solve the following 4th order nonnegative LASSO problem: $$\min_{x \geq 0} \quad || |Ax|^2 - b ||^2 + \lambda ||x||_1$$ where $|\cdot|^2$ denotes element-wise squared. $A$ is small size (e....
35 views

### Neumann boundary conditions on arbitrary surface for finite difference diffusion

I am facing the following problem, formulated in practical terms: I have a region $\Omega$ in two or three dimensions, represented as a binary mask, and an initial density $u_0$ within that region ...
59 views

### Is “Gradient Computation” in Finite Volume Discretization Really 2nd order accurate?

Based on this, pp 245, we go through these steps to discretize a gradient statement, namely $\nabla\phi$: 1- Gauss theorem reads, $$\int_V\nabla \phi dV = \oint_{\partial V}\phi dS$$ 2- Integral ...
46 views

### Demagnetizing field using scalar potential method

I want to calculate the stray magnetic field from a ferromagnet using the scalar potential method (1). The problem consists of a ferromagnetic cuboid divided into small cuboidal cells in which the ...
55 views

### How reproducible are conda environments?

I am aiming at keeping my scientific studies and analyses reproducible: I am automating them as much as possible, I am sharing them, and I sharing them together with the execution environment(s) I've ...
54 views

### Online Parameter Estimation using steepest descent

I have a first order system which is described by the following differential equation: dx/dt = -a*x + b*u where u is the input <...
78 views

### How to : numerical integration by quadrature in C language / remove NaN

What I wanna solve it the problem following ( by quadrature method ) I want to get two arrays of data ( z & tau ) from z, tau to z, tau. Since the integrand diverges at z=0.9, ...
22 views

### Metis: how to use and tutorial recommendation

I am new to METIS and trying to use it in my fortran code. I read the manual online. But still, I am not sure about how to implement it my code. I tried the test cases in the graphs directory. For ...
77 views

### Second derivative using Fornberg finite difference method

I have some discrete data, non-equispaced in x, y=f(x). I want to use a numerical finite difference method to calculate the second derivatives of y, at some point. I am using the Fornberg method, ...
41 views

### Plotting ratings matrix

Hello fellows and folks. I have been looking to do this for 1 month and still cannot find the way to do it. Here’s what’s going on: I have a csv file called ratings.csv with the following ...
35 views

55 views

### Solving a non-convex optimization problem using fmincon

I am trying to solve a non-convex optimization problem using fmincon(). At each iteration, I am iteratively looking for the optimum value and when the termination ...
53 views

### Is there a simple way of implementing dark energy into a n-body simulation?

I'm working on a gravitational n-body simulator and would like to implement dark energy into it but all I can find is papers with relativistic equations which I don't really understand. Is there a ...
40 views

### Animation using matplotlib

I am trying to animate a plot of two distinct points (blue and green points) moving about the complex unit circle using Python's Matplotlib library. The problem I am having is that the animation does ...
28 views

### PCJACOBI works but the default PCBJACOBI failed in PETSc

I am using PETSc and libmesh to solve a simple linear elastic problem with quite complicated geometry, using linear tetrahedral elements. I am always using the KSP CG as the solver. I noticed that ...
84 views

### Why would BFGS converge to a local minima of a non-convex function but maintain a large gradient?

I'm using BFGS to optimize a smooth but non-convex function $f$ that is computed by a simulation. The simulation also gives me a semi-analytical gradient $g$, which is verified by the numerical ...
81 views

### 3d vs 2d finite element method

Is the theory of 3d finite element method just an assembly of 2d finite element analysis by putting planes on top of each other, or, a much more comple and different theory applies for 3d, with ...
43 views

### Definition of Lagrange nodes in Gmsh

When gmsh uses higher-order tetrahedral elements, there is an underlying Lagrange basis used to specify the map from reference space to the element. I'm trying to load a gmsh mesh of 3rd degree ...
57 views

I have a matrix $A\in\{0,1\}^{d\times n}$ and $rank(A)=d,d<n$, and another matrix $X\in \mathbb{R}^{d\times n}$, but I do not know the rank of $X$. What can we say about the rank of their Hadamard ...
In Higham's Accuracy and Stability of Numerical Algorithms, Chapter 15, algorithm 15.3 and 15.4: The topic is ostensibly condition number estimation, but these algorithms show how to compute $\gamma$ ...