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Top new questions this week:

Numerical scheme for the level set equation that solves inverse mean curvature flow problems

I am considering the problem of simulating the evolution of an interface given as a curve in 2D (or surface in 3D) that evolves according to a velocity specified at the interface of the form: $$\vec{v}...

pde matlab numerics differential-equations advection  
user avatar asked by B0bby31 Score of 3
user avatar answered by ConvexHull Score of 4

A question related with $p$-Laplacian and conjugate gradient method

I have the following energy functional of $p$-Laplacian equation: $$ E(u) = \frac{1}{p} \int_{\Omega} |\nabla u|^p dx $$ for $2.8 \leq p \leq 5$. My goal is to minimize the energy functional by using ...

finite-difference convex-optimization nonlinear-programming conjugate-gradient  
user avatar asked by User124356 Score of 3
user avatar answered by whpowell96 Score of 2

Discontinuous Galerkin for transport equation with non-constant advection

This question is mainly an inquiry about the usefulness of Discontinuous Galerkin (DG) for the time-independent transport equation of the form $$\sigma u+\beta\cdot\nabla u =f,\;\;\;\text{on }\Omega\...

pde discontinuous-galerkin advection  
user avatar asked by UserA Score of 2

The error propagation in calculating the inverse using a matrix decomposition

I have been trying to calculate the matrix inverse of some large matrix with entries ranging by orders of magnitude. I tried to use the matrix decomposition to simplify the computation, where a matrix ...

linear-algebra error-estimation matrix-factorization inverse  
user avatar asked by ShoutOutAndCalculate Score of 2

Is the Hessian of the strain energy of a hyperelastic material positive definite in general

Is the spatial second derivative of the strain energy of a hyperelastic material positive definite in general? If this is not a general property of hyperelastic materials are there techniques for ...

optimization matrix-factorization nonlinear hyperelastic  
user avatar asked by Olumide Score of 2

Can we get the exact solution of large-scale quadratic programming problems (quadratic objective, linear inequality constraints) using KKT condition?

Crossposted at MathOverflow Consider a quadratic programming problem with the following format: $$ \text{min} Q(x) = c^Tx+\frac{1}{2}x^TDx \\ $$ $$ \text{s.t.} Ax\leq b, \\ x\geq 0 $$ where $D$ is a $...

linear-algebra optimization constrained-optimization convex-optimization nonlinear-programming  
user avatar asked by ximeng fan Score of 2

Greatest hits from previous weeks:

How do I calculate the numerical difference between two fields stored in two different VTK files with the same structure?

Suppose I have two VTK files, both in structured grid format. The structured grids are the same (they have the same list of points, in the same order), and there is a field, call it "Phi", in each VTK ...

visualization vtk  
user avatar asked by Geoff Oxberry Score of 16
user avatar answered by Geoff Oxberry Score of 16

In FEM, why is the stiffness matrix positive definite?

In FEM classes, it's usually taken for granted that the stiffness matrix is positive definite, but I just can't understand why. Could anyone give some explanation? For instance, we can consider the ...

finite-element matrix stiffness  
user avatar asked by user123 Score of 14

How can I determine the period of my pseudo-random number generator?

Suppose I'm using a linear congruential pseudo-random number generator (PRNG). Given a seed $x_0$, the multiplying factor (a), the shift factor (c) and the modulus factor (m), how can I determine the ...

user avatar asked by Paul Score of 16

Gradient descent and conjugate gradient descent

For a project, I have to implement these two methods and compare how they perform on different functions. It looks like the conjugate gradient method is meant to solve systems of linear equations of ...

optimization conjugate-gradient  
user avatar asked by Philipp Score of 12
user avatar answered by Elaine Hale Score of 18

Constraints involving $\max$ in a linear program?

Suppose $$\begin{align*} \min A &\mathrm{vec}(U) \\ &\text{subject to } U_{i,j} \leq \max\{U_{i,k}, U_{k,j}\}, \quad i,j,k = 1, \ldots, n \end{align*}$$ where $U$ is a symmetric $n\times ...

optimization linear-programming  
user avatar asked by N21 Score of 16
user avatar answered by Geoff Oxberry Score of 14

Tikhonov regularization in the non-negative least square - NNLS (python:scipy)

I am working on a project that I need to add a regularization into the NNLS algorithm. Is there a way to add the Tikhonov regularization into the NNLS implementation of scipy [1]? [2] talks about it, ...

optimization convex-optimization nonlinear-programming regression scipy  
user avatar asked by user3259573 Score of 4
user avatar answered by Brian Borchers Score of 20

Python vs FORTRAN

Which one is better: FORTRAN or Python? And I guess that in both cases you need Gnuplot, am I right? I'm working on a Windows machine at the moment. I'd like to use it to get numerical solutions for ...

python fortran  
user avatar asked by Nick Score of 20
user avatar answered by Geoff Oxberry Score of 36
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