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1500 questions
8
votes
1 answer
Linear system solution with inequality constraints - methods?
First of all, I hope I am posting this in the correct place. If not, I'm sorry and could you please direct me to where I should post this?
Problem: You are given a set of vectors, $\{\mathbf{a}^i\}_{i=1}^{24}$, and matrices $D_1$ and $D_2$ (both of…
xandrella
- 113
- 3
8
votes
1 answer
Eigenspace basis continuously depending on parameters
I have a Hermitian matrix $\mathbf{H}$ which depends on two parameters say $x$ and $y$.
When I diagonalize it at two close points $(x_1,y_1)$ and $(x_2,y_2)$ I get two close eigenvalues ($\varepsilon_1$ and $\varepsilon_2$) and two corresponding…
Maksim Zholudev
- 183
- 4
8
votes
1 answer
Newton iteration applied to nonlinear PDE
I'm having difficulty understanding how to apply Newton iteration to nonlinear PDEs and then use a fully implicit scheme to time step. For example, I want to solve Burgers equation
$$u_{t} + u u_{x} - u_{xx} = 0$$
So discretising time using a…
Matthew Cassell
- 253
- 2
- 17
8
votes
2 answers
Bracketing a discontinuity in a step function
I have the function
$f(x) = \begin{cases}
0 \:\: (x < a) \\ 1/2 \:\: (x = a)\\ 1 \:\: (x > a)
\end{cases}$,
where $a$ is unknown. I can compute the function for any value of $x$, and seek to determine $a$ (to some degree of accuracy).
Given an…
user1951162
- 81
- 1
8
votes
5 answers
Recommended Route for Mastering Inverse PDE Problems
I would like to master Inverse PDE Problems particularly with the use of Finite Elements. My problem is I don't know where to start. Should I begin by reading a book on Inverse Problems or on PDE-constrianed Optimization!
Could I get some book…
Jason
- 81
- 1
8
votes
1 answer
Shrink wrapping algorithms to make a mesh watertight for 3d printing
I'm investigating algorithms to make a mesh watertight for 3d printing. I'd be very excited to implement such algorithms. The initial input is a mesh which is not watertight and I want to understand and implement algorithms to transform it to make…
Brainless
- 203
- 2
- 6
8
votes
1 answer
Generating harmonic polynomials in cartesian coordinates
TLDR: Are these polynomials really harmonic polynomials, and how can I generate them?
Long version:
I want to describe an electrostatic potential $\Phi(x,y,z)$ over a source-free volume, by using a polynomial of the form
$$\begin{align}
\Phi(x,y,z)…
Martin J.H.
- 251
- 1
- 6
8
votes
2 answers
How to get all intersections between two simple polygons in O(n+k)
Basically the formulation of the problem I'd like to solve is very simple. Given 2 simple polygons (without self-intersections) report all intersecting edge pairs in O(n+k) time, where n - is a total number of edges, k - number of intersections…
Sergei Ivanov
- 81
- 1
- 2
8
votes
0 answers
What is the source of the error in the Sherman-Morrison formula application?
The Sherman-Morrison formula
$$ (A+uv^T)^{-1} = A^{-1} - \frac{A^{-1}uv^TA^{-1}}{1+v^TA^{-1}u} $$
results in small errors in relation to the standard matrix inverse operation after each application, as shown here. From what I understand, the…
rcpinto
- 180
- 4
8
votes
2 answers
Solving Linear Systems in Julia
To give you some context,
I am currently implementing a simple finite element solver in Julia. I am getting run-times that are 70% of a Matlab code. (Both codes are essential equivalent in structure.) I've run some profiles on my Julia code and I…
Arjun Narayanan
- 181
- 1
- 5
8
votes
2 answers
Solve non-linear set of three equations using scipy
I need to solve a non-linear set of three equations using scipy.
However, I do not have any clue on which algorithm is suitable for my problem from a mathematical point of view (stability, convergence behaviour), since scipy provides a huge variety…
albert
- 223
- 2
- 7
8
votes
3 answers
Compute smallest eigenvectors of a matrix
It appears that matlab's eigs is giving me bad approximations of the smallest eigenvectors of a matrix.
I assume I can use some slower methods which would also be more accurate...
I am looking to find the 2nd smallest eigenvector of a lapalcian…
olamundo
- 599
- 4
- 14
8
votes
2 answers
How can I numerically solve an ODE to $N$ provably correct digits?
Suppose we have an initial value problem of the form
$$ \frac{\mathrm{d} \mathbf{x}}{\mathrm{d} t} = f(\mathbf{x}) \qquad \mathbf{x}(0) = \mathbf{x}_0 $$
where $\mathbf{x}_0 \in \mathbb{R}^n$ is known exactly (i.e. to unlimited precision) and we can…
David Zhang
- 223
- 1
- 6
8
votes
1 answer
Computational methods for finding the energy eigenvalues of the time-independent Schrodinger equation with arbitrary potential
I have seen in some papers that the energy levels in some arbitrary potential are specified. How can one find the energy levels in such arbitrary potentials. For example, $V(x)=\sin^2(x/2)$ with $x\in[−3\pi,3\pi]$.
I understand that in a triple…
Sooraj S
- 153
- 2
- 10
8
votes
2 answers
Molecular dynamics simulation of water vapor?
I'm trying to do MD on water vapor. As I know there exists some water models for liquid water, such as SPC,SPC/E,TIP3P, but will they also apply to vapor state of water? And what's the difference of simulations of liquid and vapor water?
dofine
- 181
- 3