H. Rittich
  • Member for 4 years, 6 months
  • Last seen more than a week ago
Alternatives to hdf5
9 votes

HDF5 is, to some extent, a filesystem on its own. By introducing B-Trees and by the way it manages blocks, it duplicates the functionality of a filesystem. When you are running your code, you are ...

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How can I coarsen a mesh in Gmsh when 'Mesh options' include 'Refine by splitting' but nothing about coarsening?
4 votes

To create a coarser mesh, you can set the characteristic length globally to a larger value, e.g., SetFactory("OpenCASCADE"); Mesh.CharacteristicLengthFactor = 2; Circle(1) = {0, 0, 0, 1, 0, 2*Pi}; ...

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LAPACK sorting eigenvalues differently each time
Accepted answer
4 votes

You write, that you are computing the eigenvalues of a symmetric matrix. Does the matrix have real entries? In this case all eigenvalues are real, and you can use a symmetric eigenvalue solver, which ...

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What are some ideas to preprocess / precondition the following linear system?
4 votes

You have noticed that any eigenvector of $A$ is also an eigenvector of your composed matrix. When you compute eigenvectors of your matrix, you can use them in a deflation-type preconditioner, as ...

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Discretization Error amplification instead of stagnation to machine precision
3 votes

Yes. This behavior is to be expected and normal. When you are computing with a small value for $\mathrm dx$ then, to compute the difference quotient, you are subtracting two numbers that are nearly ...

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finite differences on a slanted grid --- advection diffusion equation
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3 votes

In case you can easily implement the roated grid, this is possibly the easist fix, so let me answer your question about the invariance of the convection diffusion equation under rotation of the ...

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Danger of complex arithmetic in scientific computing
3 votes

You say that the problem with complex arithmetic is that there are different ways to define the scalar product for complex vectors, compared to just one way in the real case. I think the real problem ...

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fastest linear system solve for small square matrices (10x10)
2 votes

Your question leads to two different considerations. First, you need to pick the right algorithm. Hence, the question if the matrices have any structure, should be considered. E.g., when the matrices ...

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Condition number of a matrix
2 votes

First of all, the term $\frac{\| A x \|}{\| x \|}$ is not constant. For example, consider a $2 \times 2$ matrix and let $w_1$ and $w_2$ be the columns of $A$. Then, $$ A x = x_1 w_1 + x_2 w_2 . $$ ...

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What does optimal convergence rate mean? How to prove whether a numerical method, e.g. FEM, has an optimal convergence rate or not?
2 votes

Assume you have a metric for some problem, e.g., the asymptotic convergence rate. If you can prove that there can be no algorithm that has a better value in the specific metric, then the algorithm is ...

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How to precondition FEM problems using domain decomposition?
2 votes

Let us consider the abstract linear problem $$ \mathcal{A} x = b \,, $$ where $\mathcal{A}$ is a linear operator and $x$ and $b$ some functions on a certain domain. To answer your question let me ...

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Find classical solution of transport equation with FDM
1 votes

Let me try to answer your question concerning the transport equation from a different perspective. Consider the following initial-value problem. We search for a function $v(x,t)$ such that \begin{...

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Plotting using 'colorbar' in MATLAB
Accepted answer
1 votes

The plot you have shown was probably created using imagesc. The colors were choosen with the colormap command and the color bar is shown with colorbar.

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Runge Kutta (RK4) to solve coupled harmonic oscillators
1 votes

The Runge-Kutta approximates the solution of the initial value problem $$ \dot{y}(t) = F(t, y(t)), \quad y(0) = y_0. $$ The method expects $y_0$ and the function $F$ as input. If we set $$ y(t) = \...

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