All Questions

-1
votes
0answers
21 views

How to model a hysteresis behavior using MILP on CPLEX?

The question is below: 1: y[t]=10,if x[t]>=2; 2: y[t]=-1,if x[t]<1; 3: y[t]=y[t-1],if 1<=x[t]<2. How to model the function in cplex using c++? Thank you very much! My model is added as "...
2
votes
2answers
133 views

Generate high n quantum harmonic oscillator states numerically

How can I generate the higher $n$ quantum harmonic oscillator wavefunction (in position space) numerically? Here, higher means around $n=500$, or say $n=2000$, where $n$ is the $n$th oscillator ...
2
votes
2answers
171 views

C standard for computational science

Which C standard should be used for computational science code ? Should we keep compatibility with C89/90/ANSI or jump to C99 or C11 ? Context: Code will use third-party : BLAS, LAPACK, MKL, ...
1
vote
0answers
85 views

How to simulate water, falling under gravity, and impinging on a curved surface, which is kept/present in a domain, containing air?

TL;DR: How do I simulate a hole, at the bottom of a (full) water tank? I am attempting to simulate water, flowing out of a hole/slit, at the bottom of a tank (Water Domain) (under the influence of ...
1
vote
0answers
32 views

Computing a Flux Integral in Paraview

I am currently looking into post-processing of simulation data using Paraview. I would like to compute certain integrals of field quantities. As an example, consider the following surface integral of ...
1
vote
1answer
84 views

Computing the Inverse of a matrix, using the Cholesky decomposition

I have to compute $CA^{-1}B$ and $CA^{-1}x$, where $A,B,C$ are conformable matrices and $x$ is a vector. I've read that the a very computationally stable way to compute these inverses is by computing ...
3
votes
0answers
74 views

Best way to numerically compute elliptic integrals of the third kind with complex arguments?

I need to compute elliptic integrals of the third kind with complex arguments, preferably in C++. Is there code out there to do this? I have discovered the Arb library, but that does much more than I ...
4
votes
2answers
87 views

Analytical convergent sequence and numerical divergent sequence

Is it possible to construct a sequence that converges in theory but when computed numerically with a computer program is diverging. I feel that today our computer programs doesn't allow such ...
3
votes
0answers
59 views

Block matrix and DSYRK

I want to compute the matrix $$ A = \sum_{i=1}^N v_i v_i^T $$ where each $v_i$ is a given vector of length $2500$, so that $A$ is $2500 \times 2500$, and my $N$ is about 2 million. Rather than call ...
2
votes
0answers
101 views

Efficient root finding algorithm for monotonic function

This is my first time asking a question here, so I may not be asking this in the right place. I am trying to find the roots of a monotonic function with as few function evaluations as possible. I ...
6
votes
0answers
57 views

Quadrature methods for peaky integrands

Consider $$ I = \int_{-L}^L f(x)dx, $$ where $f(x)$ is real-valued and analytic on $[-L,L]$, but it has a pole in the complex plane whose real part lies in $[-L,L]$. Call it $z_0$, and assume it is a ...
0
votes
0answers
26 views

Is this a form of stochastic gradient descent?

I want to minimize the following with respect to parameters $B$. $$\sum_{k = 1}^{K} f(A_{k}, B)$$ where $A_k$ are $K$ different data-sets and $B$ is a matrix of parameters. Can I do this by a ...
0
votes
1answer
25 views

Gmsh: Recombine 2D in script file or command line

I have many STL files and I want to reduce their size, so I use Gmsh in this way: gmsh -2 -bin -format vtk -o file.vtk file.stl -0 It reduces the size from 7 MB ...
2
votes
3answers
182 views

How does a stiff equation solver work?

I am trying to understand how stiff differential equations are solved. For instance the equation, $$\frac{\partial y}{\partial t} = \alpha\frac{\partial ^2 y}{\partial z^2}$$ can be solved using ...
0
votes
1answer
55 views

coupled equations with finite difference method

I have these three differential equations in which I need to solve numerically: $$ \frac{dn_0}{dt}= -n_0(t)W_{01}(t) + n_1(t)K_{10} $$ $$ \frac{dn_1}{dt}= -n_1(t)W_{12}(t) - n_1(t)K_{10} + n_2(t)K_{...
3
votes
2answers
87 views

DFT of $g(\omega) \exp(i C \omega^2)$. How to do it ,if uniform sampling requires too much memory?

I have a following problem : I want to transform a function $g(\omega) \exp(i C \omega^2)$. $g(\omega)$ is real and limited. It changes slowly compered to $\exp(i C \omega^2)$. I have a black box that ...
3
votes
1answer
105 views

Derivation of backward differentiation formulas(BDF)

I have been reading upon numerical techniques that are used to solve stiff ordinary differential equations. From the description given here, I could follow the steps till equation (5). I am finding ...
0
votes
1answer
73 views

Python Finite Difference Schemes for 1D Heat Equation: How to express for loop using numpy expression

Hello all, I've recently been introduced to Python and Numpy, and am still a beginner in applying it for numerical methods. I've been performing simple 1D diffusion computations. I suppose my ...
0
votes
1answer
30 views

Software for cellular automota

I would like to do simulations using cellular automata to describe the behavior of influenza. What software do you recommend?
0
votes
1answer
19 views

Binary tree for 2 elements [closed]

I want to understand Binary Search for 2 element list made of 1,2. I draw a tree as below. Is it correct? If I want to search for an element 2, it will make 2 comparisons. If I want to search for ...
1
vote
1answer
39 views

Finite difference - Explicit / Implicit / Crank Nicolson - Does the implicit method require the least memory?

Examine a dynamic 2D heat equation $\dot{u} = \Delta u$ with zero boundary temperature. A standard finite difference approach is used on a rectangle using a $n\times n$ grid. For the resulting linear ...
2
votes
0answers
38 views

Does quantum espresso and VASP use same same self-consistent-field procedure?

The codes Quantum Espresso (QE) and Vienna Ab initio Simulation Package (VASP) both use plane wave basis sets and psuedopotentials. Most of the codes in both implementation of DFT uses Fortran code. ...
0
votes
1answer
23 views

Gradient ascent method with a constant step size?

I'm trying to use the gradient ascent method on a convex function like the multivariate-Normal density function with respect to its parameters (the original is a bit more complicated), something ...
2
votes
1answer
97 views

Analytical Solution of Transport Equation

I'm looking at the analytical solution of the convection-diffusion equation $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2}-v\frac{\partial C}{\partial x}$$ with initial ...
0
votes
1answer
44 views

Simulating Brownian motion in 3-D for first hitting time?

I want to simulate Brownian motion in 3-D for the following conditions: $$p(x=0,y=0,z=0,t=0)=1$$ $$p(x,y,z=c,t)=0$$ where $p$ is the probability of finding molecules in the 3-D environment. I want to ...
0
votes
1answer
45 views

Solving Vectorial Poisson Equation in FENICS

I am trying to solve the following, "test problem" involving a vectorial Poisson equation: $$-\nabla^2 \vec{A}=\vec{J} \quad \forall x\in\Omega=[-1,1]^3$$ $$ \vec{A}=\vec{0} \quad \forall x\in\...
-3
votes
1answer
63 views

Stuck in infinite loop [closed]

...
2
votes
2answers
153 views

Best software to do big number calculations quickly

I am trying to do some work on some math conjecture. I am testing the conjecture numbers using very large math numbers (100+ digits ). I am currently using python to test these numbers. In the ...
1
vote
1answer
40 views

Step size updating scheme adaptive embedded RK methods

If I have a RK method $y$ of order $p$ and a RK method $z$ of order $p-1$ I have read I can estimate the local error as $r_{n+1} = y_{n+1} - z_{n+1}$. First of all I don't see how this estimates the ...
0
votes
2answers
58 views

TVD for temporal dicretisation

I have come across schemes where TVD (with flux limiters) is used for spatial discretisation along with Runge-kutta for Temporal discretisation. Can TVD be used for Temporal discretisation? If so ...
1
vote
0answers
55 views

Implementing boundary condition

I'm studying the transport of species A in the blood vessels, $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2}-v\frac{\partial C}{\partial x}$$ At x=0, I want to use the ...
3
votes
1answer
91 views

Golub-Kahan-Lanczos Bidiagonalization Procedure implementation doesn't produce bidiagonal matrix

I'm trying to implement the aforementioned procedure using this website as a reference. At the end of the page the algorithm is described as follows: I think I've mapped the given algorithm to code ...
1
vote
1answer
47 views

Memory and time requirements of the scipy sparse spsolve

I have a system of fairly large set of linear equations (approximately 30K equations). I am using scipy.sparse.spsolve to solve these equations. Initially, I tried ...
3
votes
1answer
55 views

Radiation heat transfer between surfaces

I'm trying to model the temperature distribution over a curved surface. Apart from the heat equation, I need to take into account the energy emission/absorption through electromagnetic radiation. The ...
2
votes
1answer
42 views

Question about strange outputs from the CVXPY solver

I am familiarizing myself with CVXPY, and encountered a strange problem. I have the following simple toy optimization problem: ...
3
votes
0answers
63 views

Library for solving multidimensional (n > 3) hyperbolic PDE systems

Does there exist a library (in any programming language) for solving (numerically) systems of multidimensional first-order linear PDEs in the form $$\mathbf{u}_{t}+\hat{A}(\mathbf{x})\mathbf{u}_{\...
2
votes
0answers
74 views

Find points that form curve segments in a point cloud

I have an ultrasonic image represented by a point cloud as shown below: I need to extract features from this image. These features can be easily recognised by a human brain since they form continuous ...
1
vote
1answer
36 views

Wrong results for $2$ stage multistep method $y_{n+2} - y_n = h\left[(1/3)f_{n+2} + (4/3)f_{n+1} + (1/3)f_n\right]$

I need to fix a code to utilise the $2$ stage multistep method : $$y_{n+2} - y_n = h\left[(1/3)f_{n+2} + (4/3)f_{n+1} + (1/3)f_n\right]$$ Since this is an implicit method, I used a Newton-Raphson ...
0
votes
3answers
73 views

Rudin lecture — if f(x) is not integrable on some interval, does it not have a Fourier Series expansion on that interval?

I found an old lecture on YouTube given by Walter Rudin (1990, in Wisconsin), and towards the beginning he mentions that if $f(x)$ were not integrable, on some interval, it would be obvious that it ...
3
votes
0answers
58 views

Given a list of intervals, find region that is contained by the largest number of those intervals

Start with 1d case. Say I have lots of 1d intervals $[s_i, e_i]$ and I want to find an interval $[s^*, e^*]$ to maximise the count of interval $i$ such that $[s_i, e_i]\supseteq [s^*, e^*]$. 1d case ...
2
votes
0answers
49 views

How to implement register blocking for 3D finite-difference stencil computations

I am in need to optimize the performance of the 3D solver that integrates a system of equations for seismic wave propagation. Unsurprisingly, the function that implements the finite-difference stencil ...
2
votes
0answers
55 views

Discrete-time Algebraic Riccati Equation (DARE) solver in C++

I need to use a Discrete-time Algebraic Riccati Equation (DARE) solver for an embedded controller (with limited processing power) in a research project and sadly, I can't find any implementation of it ...
2
votes
0answers
47 views

How to find two points within defined region in this constrained optimization problem?

I am doing a project related to robotics where I am using fmincon function from matlab to minimize the distance between the points ...
0
votes
1answer
107 views

Analytical solution of 1D advection -diffusion equation

I am looking for the analytical solution of 1-dimensional advection-diffusion equation with Neumann boundary condition at both the inlet and outlet of a cylinder through which the fluid flow occurs. $$...
2
votes
0answers
49 views

Nonlinear system with diagonal nonlinearity

Consider a nonlinear system of the form $\boldsymbol{f}(\boldsymbol{x}) = \boldsymbol{0}_{\mathbb{R}^n}$ for $\boldsymbol{x} \in \mathbb{R}^n$, where the function $\boldsymbol{f}$ is given by \begin{...
1
vote
1answer
41 views

Why is it assumed that $c_i = \sum_{j=1}^sa_{i,j}$ in the butcher tableau of a RK-method?

In my textbook it is stated that we make a "simplifying assumption" $$c_i = \sum_{j=1}^sa_{i,j}, $$ where $c_i, a_{i,j}$ are the constants in the butcher tableau. What's the relevancy of this ...
4
votes
0answers
65 views

Solution of constrained system of ODEs

Can someone point me in a direction to solve this kind of integral constrained system of ODEs. \begin{align} &\int_0^{1/2}\dot{y}^2(t)=p\\ &2\lambda_1\ddot{y}(t)+\pi cos(\pi y(t))=0\\ &y(...
1
vote
2answers
39 views

Determine conditions on parameters (for consistency) on RK method $y_{n+1} = y_n + ha_1f(t_n,y_n) + ha_2f(t_n + b_1h, y_n + b_2hf(t_n,y_n))$

I'm asked to find the conditions on the coefficients $a_1,a_2,b_1,b_2$ in the RK method $$y_{n+1} = y_n + ha_1f(t_n,y_n) + ha_2f(t_n + b_1h, y_n + b_2hf(t_n,y_n))$$ such that is consistent of (a) ...
3
votes
2answers
122 views

Parallel assembly of matrix

I have a matrix which I want to assembly quickly, which is in block form: $$ A = \pmatrix{ A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \\ A_{31} & A_{32} & A_{33}} $$ ...

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