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schrodinger eq time propagation with dissipation using split step operator

I am looking in ways to include energy dissipation while propagating a coherent wavepacket in a 1d TDSE. for example I use the split step method: exp[Δt(D+V)]≈exp[ΔtV/2]exp[ΔtD]exp[ΔtV/2], and ...
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  • 1
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22 views

Complex interpolation for isotopic (precipitation) data

Is there a package that interpolates precipitation data taking into account mountains and oceans? I have so far used Numpy and Basemap but as you can see in the code, the data from Europe affect the ...
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  • 1
1 vote
0 answers
56 views

Closed (Robin) boundaries in advection-diffusion equation with FDM

I am solving the equation $$ \frac{\partial \phi}{\partial t} = \frac{\partial}{\partial x} \left( D \frac{\partial \phi}{\partial x} + v\phi \right) $$ using finite differences. I want to include ...
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0 answers
43 views

I was appointed to a competition but I'm not familiar CS, I'm more familiar with programming. What should i do? [closed]

I'm currently in a Junior High School level and our club adviser asked me to join in a competition under MATHEMATICS AND COMPUTATIONAL SCIENCE, the problem is that i'm not into computational science ...
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0 answers
19 views

Add tikz terminal to gnuplot [closed]

Recently, I installed gnuplot5.4.3 in ubuntu 21.10. My mistake is not to create a symbolic link before launching ./configure to use ...
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1 vote
0 answers
41 views

How can I reduce the artifact in "Thin Plate Spline" interpolation?

At the Top "right", there is the 2D-density plot of the recorded data (actual), fewer in number. On the top-left is the interpolated data (thin-plate), i.e. larger in number. Compared to the ...
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-2 votes
0 answers
53 views

Using Implicit Euler Method with Newton-Raphson method

So I'm following this algorithm and here is my attempt: ...
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0 votes
0 answers
26 views

How does one approach solving these ?(parallel processing problem) [closed]

I'm not entirely sure what is required of me. If anyone recognizes these types of problem, or where I can learn more about this topic and these types of problems, or what subject this even is covering,...
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-1 votes
1 answer
63 views

Billiard reflection inside a triangular mesh

I am currently interested in billiards and their trajectories. I would like to simulate a billiard inside a water-tight mesh. A mesh basically consists of a list of points in 3D space (vectors with 3 ...
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  • 99
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1 answer
49 views

Efficiently solving SDP relaxation of an integer quadratic program

I have an integer quadratic program of the form, \begin{align} \underset{x}{\max}&\;\;\|Ax-b\|_2^2\\ \text{subject to}&\;\;x\in{\bf Z}\geq0 \end{align} I'm currently using the (admittedly ...
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0 answers
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Reference request for finite elements theory

Consider a domain $\Omega \subseteq \mathbb{R}^{2,3}$ which is non convex and with $C^2$ boundary. Could you recommend a good reference where it is explained how: without needing isoparametric ...
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  • 101
-1 votes
1 answer
28 views

Add variable electric potential in Comsol [closed]

I have a model in Comsol where some part has a fixed potential (-800v) while the other is grounded. Does anyone have an idea on how to change the potential alternately from +800v to -800v with a ...
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2 votes
0 answers
91 views

FEM applied to heat equation and incompatible conditions

Consider the problem $$u_t - \Delta u = f \text{ on } \Omega\times (0,T)\\u=0 \text{ on } \partial \Omega\times (0,T) \\ u(x,0)=g(x) \text{ on } \Omega$$ with $g$ NOT vanishing on the boundary. If I ...
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  • 21
1 vote
0 answers
32 views

Lattice Boltzmann methods beyond BGK-style collision operators

I am trying to educate myself on the lattice Boltzmann method to see if it may be useful for simulating some problems in plasma physics that I am interested in. One thing that strikes me is the (...
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2 votes
2 answers
99 views

Adaptive computation in neural ODEs

I have been reading the neural ODE paper and I understand that neural ODEs have a continuous depth model structure. And I understand the fact that they are especially very useful for time-series data. ...
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4 votes
3 answers
409 views

What condition ensures the global continuity of the solution in the FEM?

I know this is trivial but I don't seem to understand it. In which step of the FE formulation do we enforce the global continuity of the solution? Or in other words, how the construction of the local ...
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-1 votes
1 answer
46 views

Fitting gauss-hermite-parametrization to data?

I want to fit this data. I have the following model functions. Classic gaussian: def gauss_model(x, mu, sigma): return np.exp(-0.5*((x-mu)/sigma)**2) And ...
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-2 votes
0 answers
38 views

Setting up boundary conditions to solve PDEs using method of lines

Objective: To add boundary/initial conditions (BCs/ICs) to a system of ODEs I have used the method of lines to convert a system of PDEs into a system of ODEs. The ODEs themselves involve a lot of ...
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0 answers
53 views

Is there a mathematical algorithm that can determine whether a problem is parallelizable?

Is there a mathematical algorithm that can determine whether a problem is parallelizable? Possibly similar to how the definition for "computable" works out: https://en.wikipedia.org/wiki/...
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  • 379
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0 answers
30 views

3D Euler Bernoulli Beam for Nonlinear FEA

Anybody has any experience in coding 3D beam elements? I am trying to write a C++ code for a 3D euler bernoulli beam. For 2D, I used Reddy for coding 2D for non linear FEA. How should I proceed with ...
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0 answers
66 views

The mathematical meaning of a zero gradient pressure boundary condition in the Navier-Stokes equations

I would like to solve the Navier-Stokes equations for the unsteady problem of the flow around a circular cylinder. I would like to understand how to write mathematically the boundary condition for the ...
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3 votes
1 answer
79 views

Using submatrices of matrix decomposition for solving a large number least-squares problems

I want to decrease the computational time for solving a large number (>1000) of least-squares problems. Given a matrix, the system matrix for each least-squares problem is a submatrix of the given ...
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  • 119
1 vote
1 answer
72 views

constructing a symmetric matrix for finite difference

I come across the following operator in a paper $\mathcal{I}\psi = \psi_{xxxx} + (r~\psi_x)_x$, where $\psi=\psi(x)$ and $r=r(x)$. Periodic boundary condition is employed. It claims that the operator $...
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  • 217
0 votes
1 answer
41 views

Nearest neighbours with a subset structure

I have a set of points of $\mathbb{R}^2$ which is organised in subsets: $$ \cup_{0\leq i<N} \left\{ P_i^j \in \mathbb{R}^2, 0\leq j<M \right\} $$ For all $(i,j)$, I want to find $P_k^l$ in ...
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-1 votes
0 answers
56 views

Solving Burger's equation using second-order central upwind

I am numerically solving a Burger's equation with second order semi-discrete central upwind $$u_t+\left(\frac{u^2}{2}\right)_x=0$$ with the initial condition $$u(x,0)=\frac{1}{4}+\frac{1}{2}\sin(\pi x)...
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2 votes
0 answers
62 views

How to accelerate the computing of implicit finite difference method for heat conduction between two solids

Edit on May 3rd: I have found the problem. Because the difference of between $k_1$ and $k_2$ is huge, a very small time step need to be chosen so that the right green part can "feel" the ...
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2 votes
1 answer
94 views

How to ensure the numeric value is always positive in Optimization Python?

I am currently performing optimization onto a quadratic function by manually coding the algorithm: $$\min f = x^T v x - r^T x\\ \text{subject to } x \geq 0\, .$$ Here, optimizing the function without ...
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1 vote
1 answer
89 views

Huygens Fresnel Diffraction integral using dblquad in python

I am attempting to create a python function to assist in calculating the following numerical integration of the Huygens Fresnel integral in the form of ...
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0 votes
1 answer
88 views

Suming up the series $1+1/2+...+1/n$ in C [closed]

...
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3 votes
0 answers
71 views

How can I improve this matrix product calculation in OpenCL?

I am trying to compute a matrix-matrix product of N stacked complex double N x N matrices. For simplicity, I assume N = 512. I have written code in C++ parallelized with OMP and using OpenBLAS for the ...
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  • 31
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0 answers
40 views

Numpy random generator seed choice

I am new to understanding pseudorandom number generators and sometimes feel daunted by them. For some time I have used the following approach in my work: In one file, I'd have ...
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1 vote
1 answer
47 views

FORTRAN coding question [closed]

I am contacting research and I came across an algorithm in FORTRAN, with which I am not familiar. For the code above I have two questions: What does "DO 1 (...)" mean? I see that there is ...
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  • 11
1 vote
0 answers
25 views

cuSolver Sparse solver fails with CUSOLVER_STATUS_INTERNAL_ERROR [closed]

I'm endeavouring to use cuSolver to solve a sparse linear system. But when I run my code, it fails with CUSOLVER_STATUS_INTERNAL_ERROR. What's going wrong? How does ...
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  • 3,091
3 votes
0 answers
66 views

Numerical algorithms made stable by unums which are unstable on IEEE floats

For unums, there is good evidence (see figure 5) that accuracy is better than IEEE floats. (Note: I use the term "unum" broadly to refer to any of the various iterations and revisions to the ...
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  • 2,001
0 votes
0 answers
28 views

Complexity of primal-dual interior-point in terms of "Big O"

How can I get the Big O complexity of a convex continuous problem solved using MOSEK, and includes M continuous variables. I know that MOSEK uses primal-dual interior-point to solve it, but I am not ...
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0 answers
25 views

Complexity of Branch-and-cut algorithm in terms of "Big O"

How can I compute the Big O complexity of the Branch and cut algorithm? I am solving an integer linear program using MOSEK that includes $M$ binary variables, but I do not know how to calculate the ...
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0 votes
1 answer
29 views

Get the equilibrium value in coupled ode by python

I am dealing with a coupled ODE. I have already plotted the solutions out using odeint, but I want to get the value of equilibrium. The ode looks like this: ...
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0 votes
0 answers
63 views

How to solve spatially discretised PDEs (method of lines) in solve_ivp or ODEint?

I can discretise the spatial domain of a system of PDEs using the method of lines, converting the system of PDEs to a system of ODEs (with a time derivative only). These equations (for context they ...
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-2 votes
0 answers
49 views

ADI method for a 2D advection-diffusion equation

I have discretized energy equation (2D advection-diffusion equation) with ADI (Alternating Direction Implicit) method, like: $$\frac{\partial\theta}{\partial t}=\frac{\partial^2\theta}{\partial x^2}+\...
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1 vote
2 answers
116 views

Secant Method for finding $\sup f^{-1}(0)$

Let $f \in C^0[0, 1]$, and suppose $f \ge 0$. How can I compute $\sup f^{-1}(0)$ efficiently?
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  • 119
-1 votes
0 answers
17 views

Mixed number for relaxation time, equilibrium function and density in lattice Boltzmann method

I am simulating the turbulent model in a pipe with a constriction. when I am applying the second-order bounce back method for none slip boundary, all variables will get the mixed number form after ...
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-2 votes
0 answers
22 views

How can I generate time series band-limited white noise for a given give voltage-amplitude distribution over desired frequency band in Python?

...
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1 vote
1 answer
59 views

Nonlinear integral equation on the half line

I want to numerically solve the following equation for $\phi$ on $\mathbb{R}_+^{*2}$: $$ \partial_t \phi (w, t) = \int_0^{+ \infty} k(\alpha w + \beta w', w') \phi(\alpha w + \beta w', t) \phi(w', t) ~...
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  • 433
1 vote
0 answers
67 views

scipy.optimize.minimize fails to converge but result is OK

I am trying to optimize a non-linear least squares problem with scipy.optimize.minimize. I have simplified my actual problem down to the case where I am just computing the top 'principal components' ...
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  • 119
2 votes
0 answers
63 views

Numerical scheme for the heat equation on the icosahedral hexagonal grid

I have a predefined grid(like this) that is spawned from a regular icosahedradron. It consists of many hexagons and 12 pentagons (corresponding to icosahedradron vertexes). I can tweak the granularity ...
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0 votes
0 answers
73 views

optimization problem with L2-norm constraint

I am currently trying to solve a regression problem, which leads me to an optimization problem. Say that we have measured data ($\hat{S}(\omega)\in \mathbb{C}^{N\times N}$), and each entry of this ...
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  • 1
2 votes
1 answer
65 views

How can we model time progress in linear programming?

I am trying to solve a scheduling problem with linear programming. I have N disks that each have a capacity of constant C. At each time interval t_i, a set of write requests with different sizes ...
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1 vote
2 answers
80 views

Simulate Jump-Diffusion $dX_t = \mu(X_t)dt + \sigma(X_t)dW(t) + \int_{\{|c| <1 \}}g(X_t,c)\tilde{N}(dt,dc) + \int_{\{|c| \ge 1 \}}h(X_t,c)N(dt,dc)$

I would like to be able to model an SDE having the form $$dX_t = \mu(X_t)dt + \sigma(X_t)dW(t) + \int_{\{|c| <1 \}}g(X_t,c)\tilde{N}(dt,dc) + \int_{\{|c| \ge 1 \}}h(X_t,c)N(dt,dc).$$ where $W$ is a ...
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3 votes
0 answers
73 views

Are there radial basis functions $\phi_n(x)$ which can be factored as $f_n(x) x^{\alpha}$ for $0<\alpha<1$ and $n>0$?

I am looking for a set of radial basis functions $\phi_n(x)$ on $\mathbb{R}^+=[0;\infty[$ which satisfy some othogonality condition $$ \int x \phi_n(x) \phi_{n'}^*(x) dx =\delta_{nn'}$$ and "...
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0 votes
0 answers
36 views

Solving Symmetric/Hollow Matrix issue

I have a particular issue and need something creative or solution from calculus. I have Symmetric/Hollow Matrix, a numbers are % of mismatch between them. Ideally, all of them should be 0, but I have ...
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