# All Questions

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### (Isoparametric) Mapping of physical coordinates to their equivalent parametric coordinates on a reference element

I have some experiece with finite element methods (FEM), in general. However, I mainly worked with Cartesian grids -- i.e. using orthogonal (non-curved) elements. Recently, I became interested in a ...
• 103
24 views

### 1D FDTD simulation of plane wave propagation and the Courant stability condition

I'm currently trying to simulate a simple case of wave propagation in free space before adding in more complexities, and already I'm stumped. I understand the Courant stability condition. However, I ...
28 views

### Good references for the P3/P1dc element

I am struggling to find some good references for the P3/P1dc element (cubic element for velocity and linear piecewise discontinuous for pressure) for the Stokes/Navier-Stokes equations. Is there a ...
• 964
43 views

### Source for scalability challenge for number of finite element nodes per process

Context In distributed simulation of a finite element mesh with $N$ nodes and $P$ processes, a professor stated to me that "achieving good scaling for more than 25,000 finite element nodes per ...
26 views

### Fastest way to calculate the eigenvector with the largest eigenvalue for a 3*3 positive-definite matrix

As stated in the title: I have a 3 by 3 positive-definite matrix $M$. What I need is the eigenvector corresponding to the largest eigenvalue, since I am calculating the solution to maximize the value ...
• 101
34 views

### Estimating the rate of convergence of Projected Gradient Descent on constrained polynomial objectives

I am estimating the order of convergence of Projected Gradient Descent (GD) on quadratic polynomials with random coefficients independently drawn from Uniform(-1,1) and bounded by a unit hypercube. I'...
• 21
38 views

### Datasets for inverse heat transfer problems

I was wondering if there is an available, real-life known inverse heat transfer problem dataset to benchmark oneselfs algorithm, as in MNIST for deep learning. Talking about... (well in this case I ...
• 181
1 vote
43 views

### Solving TOV equations that describes neutron stars in modified f(R, T) gravity

Sorry for the long post, tldr at bottom. I'm trying to use standard RK4 code in C/C++ to solve a coupled system of 2 modified TOV equations in f(R,T) gravity and reproduce some of the results of this ...
• 23
136 views

### Finding ALL Eingenvalues of a Sparse Integer Matrix

I would like to find ALL Eingenvalues of a huge, very sparse integer matrix. This matrix has a lot of known properties, e.g. that it is symmetric and nearly tridiagonal, with very few (max. ca. 4 per ...
56 views

1 vote
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• 185
41 views

### representing firing rates of a neuron using delta functions [computational neuroscience]

I'm reading 'fundamentals of computaional neuroscience' by Thomas P. Trappenberg and was confused while reading about representing firing rates using direc delta functions. instantaneous firing rate ...
1 vote