# Questions tagged [numerics]

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### Questions on the theory of distributed numerical algebraic computation

I'm trying to build a pure python distributed numerical algebra computation kernel based on GPU. but after I've learnt most of the software engineering, I realise that I'm seriously lacking in ...
78 views

### Using Crank-Nicolson to solve Non-Linear Schrödinger equation in Python

I aim to solve the (non-linear) Schrodinger equation using the Crank-Nicolson method in Python. Here are my two functions. ...
35 views

### recommendation on some papers/books about frontal solver used in FEM

I'm reading a program about computational plasticity, this program use frontal solver to solve the program, but I'm not familiar with frontal solver even after reading some papaers, so could you ...
43 views

### How do you build a polyharmonic discrete system?

Polyharmonic equations, to my understanding, are defined as: $$\Delta ^k u = 0$$ i.e. one repeatedly applies the laplace operator to the function a certain number of times and the result must be 0. ...
53 views

### Discretization of generalized kinetic term in 2D Poisson partial differential equation

A typical 2D Poisson PDE is given as $$\nabla^2\varphi(x, y)=f(x, y)$$ where the Laplacian term, $\nabla^2\varphi$, can to some degree be interpreted as the kinetic energy (given proper scaling) (...
35 views

1 vote
446 views

### PhD in scientific computing to be a scientific programmer

Intro and disclaimer: this question concerns developing a career in Scientific Computing in industry, starting from an (applied) mathematics background, say an MSc. It definitely arises from my ...
83 views

### Deformation matrix, Math hack for stability on large simulation steps?

So there is a numeric technique for updating a deformation gradient in MPM that goes as: $$F_{n+1} = (I + \nabla \vec v \Delta t)F_n$$ This works for small time steps but for large time steps ...
1 vote
88 views

### Improved euler on hybrid methods where both time and space are discretized?

I am trying to understand how to use the improved euler method on MPM simulations. In the kind of MPM simulation I am doing with forward euler the order of operations is as follows: Write particle ...
78 views

### Verlet integration on grids or how to get better stability in hyperelastic simulation

I am using MLS-MPM to simulate both solid and fluids. It works, but the amount of time steps I must do for hyperelastic solids is absurd. To give you some perspective, I am able to simulate just the ...
241 views

### How to plan convoluted measurements

I have a physical function $f(x)$ which I intend to measure. Problem is that I cannot read it directly, but through a response function $g(x)$ which is known to me with great accuracy and any one ...
1 vote
96 views

### Isolating decaying solutions to nonlinear second-order ode

I need to solve a nonlinear ODE of the form $$\frac{d^2 y}{dx^2} + \frac{1}{x}\frac{dy}{dx}-\frac{1}{x^2}\sin(y)\cos(y)+\frac{2}{\alpha}\frac{\sin^2(y)}{x}-\sin(y)=0$$ numerically, subject to the ...
147 views

### Approximating the solution of a non-linear ODE using Python

This is my first time asking a question here, so please tell me if I have made a mistake or if anything is unclear. I am working on my high school research project on the motion of a ball falling ...
115 views

1 vote