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Tracing Exact Path And Uncertainties Involved

If for instance suppose we take a situation like this- A satellite just exploded due to some reasons and it's sharpnel are falling in Earth. We have to find out the exact location where they will ...
25 views

Why don't we call the simulation “a model for …”?

When a set of model equations, e.g. some coupled differential equations, has solutions that behave in ways similar to real-life phenomena such as blood flow in the heart, a wave movement, or a plate ...
16 views

How to use QZ decomposition for single matrix in Matlab?

Can I use QZ decomposition on a single square matrix in Matlab? Like, [Aa,Q,Z]=qz(A);
30 views

Optimization algorithm / approach for suggesting what goods to buy and sell in a marketplace?

A toy problem would probably be best to explain it this. Let's say we have 100 people, each with 4 unique types of items (to simplify things, let's say it's the same four types of items for each ...
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Classical vs. modified Gram-Schmidt

It is often said that modified Gram-Schmidt is more robust with respect to rounding errors than classical Gram-Schmidt, but it is very hard to find a good explanation / example of why this is so. Can ...
24 views

How to define $P0-$ Piecewise constant basis function in finite element method?

Suppose if we take $X_h(G)$ as finite element space then this space (space of piecewise constant basis function)is defined as $$X_h=\{v: v|_{T}=c_{T}, T \in \mathbb{T}\},$$ where $\mathbb{T}$ is a ...
345 views

What's the terminology for this alternative minimization algorithm?

Say the model is $F(x_1)G(x_2)Z(x_3) = y \in \mathbb{R}^N$, with $F,G,Z$ explicitly known, we are given observation of $y$ as $y_b \in \mathbb{R}^N$ to find the value of $x_1$, $x_2$, $x_3$ for each ...
26 views

Cubature rule in unit Sphere in $\mathbb{R}^{3}$

I need to find the cubature rule for the following integration $$\int_{S^{2}} f(s,\tilde{s})d\tilde{s} ds,$$ where $S^2$ is the unit sphere in $\mathbb{R}^{3}$.
23 views

Calculating the Convolution using FFT

I have the following convolution as part of a numerical simulation. $$T(r)=\int d^3r_2 p(r_2)f(r_2)\alpha(r-r_2)$$ My problem is that the analytical expressions for $f$ and $p$ do exist but, I have ...
10 views

Error on the fit parameters when several good fits exist

I am using the reduced chi-squared statistic to determine the goodness of fit. I run several simulations and determine that a parameter 'p' has a certain range of values that all give values between 0....
37 views

Finding curves where function goes to zero in two dimensions

Suppose $f(x,y)$ is a complex function of two real arguments with roots* that are not discrete points but lie in curves. (Is there are term for this characteristic?) An example is shown below: the ...
62 views

Sensitivity of BFGS to the accuracy of the gradient

I am studying how to speed-up the BFGS method using quantum computing techniques. I have used a method of speeding up the gradient of the function, but it sacrifices the precision value of the ...
34 views

Givens rotation vs 2x2 Householder reflection

The usual story of Givens rotations vs Householder reflections is that Householder reflections are better if you want to map a long vector to $e_1$, while Givens is better if you want to map a 2-...
19 views

Fast convergence of smoothing of periodic noise

I have essentially periodic data from a simulation (not exactly periodic but is qualitatively fairly periodic), and I'd like to take an average or noise filter of some sort that I can get a well ...
41 views

How to include penalty in a Objective Function with Python? GEKKO

I'm trying to include a "great M" penalty in my objective function. I want use the entry x vector values as entry values in a function. A fixed maximum value is took initially for the returned value ...
55 views

Best way of storing numerical data in a compact manner, while leaving it accessible for tools like GnuPlot?

My simulation, written in C++, generates a large amount (roughly ~500) of text files for each set of parameters I try to simulate, with four columns of ~5k double values in each file. Furthermore, to ...
253 views

Iterative linear solver for “ugly” saddle point system

I am a graduate student majoring scientific computing. The numeric model I made caused a very ugly-looking saddle-point linear system. It is not symmetric at all and I will attach the sparsity pattern ...
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MINLP with GEKKO - Modeling discrete variables

I'm trying to define a MINLP optimization problem with GEKKO in Python, and I want to use some variables with fixed values. For my first variable, x1, I need to define the following values (as would ...
30 views

3D log density plot in ParaView

I have a .csv file of thousands of (x,y,z) point particles that I would like to visualize in ParaView. I am able to plot a 3D scatterplot using the TableToPoints, and by decreasing point opacity I can ...
21 views

Need suggestions about technical difficulties - Drying + Pyrolysis of coal particle

In OpenFOAM by default, the FireFOAM is well supported for solid pyrolysis modeling. With that in mind, I managed to built my solver for a modified version of pyrolysis (for dry coal - without ...
42 views

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Fast iterative approximate order-oblivious Orthogonalization algorithm?

I have set of N m-dimensional vectors $\{\phi_i\}$ which gradually loose mutual orthogonality in an algorithm. => I have to re-orthogonalize them every few iterations. But if I do e.g. Gram–Schmidt ...
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Is there a library that allows einstein summation on dense, sparse, and LinearOperator type tensors

Numpy's einsum only works with dense tensors. Is there an alternative that also works with sparse tensors and linear operators? For example, I might have a ...
32 views

What is the best methodology for physics simulators of large floating base rigid body systems?

I want to implement a physics simulator for large floating base rigid body systems from scratch. The Rigid Body Dynamics Systems (RBD) should typically have the following characteristics: About ~50 ...
76 views

An optimization method for bounding the eigenvalues of a unknown non symmetric matrix

Given a positive objective function $f$ that acts on a real-valued matrix $A$, I am interested in the following problem \underset{A \in \mathbb{R}^{n \times n}}{\text{minimize}} \quad f(A) \quad \...
37 views

Doing computations on a very large numpy array: streaming the calculation vs out-of-core memory

I am trying to perform a calculation in numpy that depends on several parameters, and involved the creation of many intermediate arrays. These intermediate steps involve integrals over more parameters....
I'm trying to solve 1D Euler equations with gravity in spherical coordinates using a finite-difference TVD MacCormack method on a non-uniform grid of $N$ components, following the method provided in ...