# All Questions

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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 ...
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 ...
1 vote
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 ...
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 ...
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 ...
• 101
1 vote
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 ...
53 views

### Using Implicit Euler Method with Newton-Raphson method

So I'm following this algorithm and here is my attempt: ...
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,...
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 ...
• 99
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 ...
• 443
46 views

### 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 ...
• 101
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 ...
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 ...
• 21
1 vote
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 (...
• 695
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. ...
• 23
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 ...
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 ...
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 ...
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/...
• 379
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 ...
• 11
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 ...
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 ...
• 119
1 vote
72 views

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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