1
vote
0answers
10 views

Estimation of time taken to reach steady state in an MD simulation of Poiseuille flow

I am trying to do a Molecular Dynamics Simulation of a complex fluid, confined between solid surfaces. I would like to find the flow rate as a function of fluid film thickness, $h$, for a plane ...
1
vote
0answers
13 views

similarity/distance measurement between two ranked sequence

Is there an efficient way to measure similarity/distance between two sequences of ranked numbers/letters. The two sequences are of different length, and only have some elements in common? For ...
1
vote
1answer
56 views

Quadrature order for finite elements and time dependent discontinuous Galerkin

When setting up a finite element system you have to use quadrature to calculate the integrals. I'm having trouble understanding what order rule to use. I know of some rules of thumb, for example with ...
2
votes
0answers
35 views

Implementation of no-slip boundary conditions in lattice Boltzmann method fluid simulation

My faculty advisor recommended that I take a look at the lattice Boltzmann method as an introduction to scientific computing and potentially an undergraduate honors thesis topic. I cooked up a some ...
0
votes
1answer
53 views

Reference request for matlab

I am a complete beginner in computing and I am trying to learn some computing skills. I am learning how to use Matlab as my first programming language. Are there are websites that have notes for ...
1
vote
1answer
37 views

On the flight/matrix free SVD of large sparse matrix

I am trying to apply SVD to large sparse matrices. I already compared the performances of Propack and irlba to those of the matlab svd and svds. These two packages enhance significantly the computing ...
1
vote
0answers
27 views

What is the best way to stop an asynchronous-heterogeneous MPI program?

I want to stop immediately an MPI program, that has N processors and each processor runs a different program (with different computational complexities). Processors share information to each other ...
1
vote
0answers
33 views

Comparison between of higher order interpolations

A while ago I came up with an algorithm which can be used to numerically solve optimal control problems, which basically came down to discretizing the control input $u(t)$ and interpolating this to ...
0
votes
0answers
27 views

CAS Problem with integrals

I got this problem thrown at me, unfortunately I lack context at the moment but I thought Maple or Mathematica would solve it anyways. I have a function $f$ over $x$ and $y$ such as this (Maple) ...
0
votes
1answer
41 views

adjoint method package for ODE(PDE)-constrained optimization

I have this type of question (ODE-constrained optimization) to solve: $g(x,p)=0$ is the simulation, where $x$ is state variable and $p$ is parameters aimed to optimize; $f(x)$ is the objective ...
0
votes
1answer
47 views

bifurcation diagram MATLAB runs out of memory

I have a 3000 x 2301 matrix 'xfinfin' in MATLAB that I want to plot in the following way: ...
0
votes
0answers
38 views

CFL Neccessary Condition

The theorem states that if a difference scheme converges then it necessarily satisfies the CFL condition. How can this be proved?
1
vote
0answers
31 views

Manipulating/Extracting Data and Developing Methods - Language Choice [on hold]

As a general programming enthusiast and aspiring Bioinformatician student I have an intermediate understanding of computing (languages) as well as Java, and to a lesser extent C++. Having knowledge in ...
3
votes
0answers
53 views

Solving an ODE using shooting method

I have been trying to solve the following nonlinear ordinary differential equation: $$-\Phi''-\frac{3}{r}\Phi'+\Phi-\frac{3}{2}\Phi^{2}+\frac{\alpha}{2}\Phi^{3}=0$$ with boundary conditions ...
9
votes
2answers
109 views

Multigrid on “not perfectly rectangular” grid

Multigrid introductions normally use a rectangular grid. Interpolation of values is then straight forward: Just interpolate linearly on the edge between two adjacent nodes of the coarse grid to find ...
0
votes
0answers
15 views

Laplace Operator with PyNFFT

I am learning to use PyNFFT for nonuniform FFT. I try to apply the laplace operator to functions. As a test, I want to take $f(x) = \cos( 2\pi i k \cdot x)$, calcualte (using the package) $\Delta f$ ...
4
votes
1answer
91 views

Test of 3rd-order vs 4th-order symplectic integrator with strange result

In my answer to a question on MSE regarding a 2D Hamiltonian physics simulation, I have suggested using a higher-order symplectic integrator. Then I thought it might be a good idea to demonstrate the ...
2
votes
2answers
87 views

Ill-conditioned Jacobian matrix from Nernst-Planck equation with Butler-Volmer reactions

The governing equations are listed here of my notes on page 4. It's a reproduction of other's paper which solves the equations with COMSOL. The problems arise when I want to solve for the consistent ...
2
votes
2answers
58 views

What's the role of visualization?

I'm just starting at scientific computing and I'm seeing that results can be generated merely by plotting the variables. Of course more variables lead to more axes/dimensions so e.g. a three variable ...
1
vote
2answers
74 views

Building minimization optimization problem for 2nd-order elliptic PDE

I am solving elliptic PDE problem, for which, Euler scheme looks as following: $$ \nabla [\gamma ( |\nabla u|^2) \nabla u] = 0,$$ where $$\gamma(|\nabla u|^2) = (1 + |\nabla u|^2)^{-1/2}. $$ I am ...
4
votes
1answer
44 views

Optimal partitioning of a graph

Consider a planar graph, where each node is associated with a weight. I would like to partition the graph such that the sum of the node weights in each group satisfy a minimum requirement. However, I ...
2
votes
0answers
83 views
+50

Diffrence between moving least square and weighted least square in interpolation

Could you explain exact difference between moving least square (MLS) and weighted least square (WLS). I personally feel that moving least square is a sub case of weighted least square. My ...
1
vote
1answer
42 views

FENICS subdomains - restriction/ prolongation operators

I am trying to implement my own multigrid method in fenics. Is there any "smart/ fenics" way how to assemble subdomains and obtain restriction/ prolongation operators ? Thanks!
2
votes
2answers
73 views

How to efficiently implement Dirichlet boundary conditions in global sparse finite element stiffnes matrices

I am wondering how Dirichlet boundary conditions in global sparse finite element matrices are actually implemented efficiently. For example lets say that our global finite element matrix was: $$K = ...
3
votes
0answers
29 views

Flux at coarse-fine mesh grid interface?

I am trying to solve one dimensional inviscid Burger's equation using adaptive mesh refinement. This is the PDE: $$\frac{\delta U}{\delta t} + \frac{\delta F}{\delta x} = 0$$ where the flux F of the ...
0
votes
1answer
62 views

Decoupling integral $\int f(x+ y )-f(x) dy = \int f(x+y) dy - \int f(x) dy$ in a numerical integration scheme?

Let us say I want to compute the following expression by a numerical integration scheme: $$ I = \int^{-x}_{-\infty} f(x + y) \, \mathrm dy - \int_{\mathbb R}\bigg(f(x+y) -f(x)\bigg)\, \mathrm dy $$ ...
0
votes
0answers
5 views

Log-out on Computational Science [migrated]

Is it possible to log out from this website? I am trying to find the log out button - but not very successfully.
2
votes
0answers
47 views

preconditioned Uzawa method with Petsc

I am trying to improve the resolution of a Stokes problem (P2/P1 on unstructured mesh) defined by the matrix $M$: $M= \begin{pmatrix} A_u & 0 & B_u \\ 0 & A_v & B_v\\ B_u^T & ...
0
votes
0answers
23 views

Optimization of a molecular dynamics coarse grain model

I am trying to optimize a model I develop for molecular simulation, however, I have zero experience in optimization and I need some guidelines in approaching the solution. I basically do not know ...
1
vote
1answer
61 views

Linear vs Non Linear inverse problems: Does non-linearity help?

This is not a typical question with a deterministic answer. If this is not the right place, feel free to close it. For the past one year I have been working on various kinds of inverse problem. Most ...
3
votes
0answers
29 views

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 ...
1
vote
0answers
84 views

Minimal surface finite differences problem - Matlab assemble

I face to the following problem: $$(1+u_x^2)u_{yy} - 2u_xu_yu_{xy} + (1+u_y^2)u_{xx}=0.$$ Problem needs to be discretized and assembled. Does anybody know how to proceed in Matlab?
0
votes
1answer
99 views

Why is Godunov's scheme (for the advection equation) diffusive?

I'm trying to solve the advection equation $$m_t+(\alpha m)_x=0$$ with $m(0,\cdot)=m_0$ numerically using the first order Godunov scheme. Hence I write ...
2
votes
0answers
29 views

Hessian eigenvalues in 4D-VAR data assimilation

I am using variational data assimilation (4D-VAR) to estimate emissions of anthropogenic greenhouse gases using a rather complex atmospheric transport model. Hence, the optimal solution to my problem ...
1
vote
0answers
57 views

Transfer Matrix Method in a rectangular potential well

I am trying to follow an algorithm that is described in Elementary Quantum Mechanics in 1D. I want to compute eigen-energies and functions in bound states in the basic case in rectangular potential ...
1
vote
0answers
39 views

A better way to compute a double integral involving a infinite series?

Let $D_{\nu}(.)$ is the parabolic cylinder function (http://mathworld.wolfram.com/ParabolicCylinderFunction.html) And $\Gamma(.)$ is the Gamma function. Define ...
2
votes
1answer
49 views

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 ...
5
votes
3answers
69 views

Does the Lanczos starting vector have to be random?

In all descriptions of the Lanczos vector, it's said that the starting vector is random. But let's say I'm only interested in the eigenvector associated with the lowest eigenvalue (as is the case ...
3
votes
1answer
67 views

Computing Fourier representation of space dependent advection operator via FFT

Consider the following equation on the circle: $$\dfrac{\partial p(x,t)}{\partial t} = a(x)\dfrac{\partial p(x,t)}{\partial x} \equiv L(p) \enspace ,$$ where $L$ is the operator acting on $p(x,t)$. ...
3
votes
1answer
55 views

Sparse Matrix Reordering

Matrix reorderings are important for many direct solvers. Sometimes the objective is to reduce the bandwith or the generated fill in by LU Decomposition. I am interested in a reordering which reduces ...
1
vote
1answer
27 views

Spatial evolution of kinetic energy in free surface flow in terms of values on boundary

I'm running a potential flow solver, and I have values of the velocity potential $\phi$ on the boundaries. I'd like to compute the spatial evolution kinetic energy in the system. In particular, I'd ...
1
vote
0answers
30 views

Optimization with matrix exponential constraint

Suppose I'm optimizing for an unknown $x\in\mathbb{R}^k.$ I have a linear operator $A(\cdot)$ that maps $x$ to an $n\times n$ symmetric matrix, i.e., $A:\mathbb{R}^k\rightarrow\mathbb{R}^{n\times ...
4
votes
1answer
118 views

Appropriate iterative linear solver for an eigenvalue problem

I'm trying to solve a generalized eigenvalue problem $$Ax = \lambda Bx, \quad A = A^\top > 0,\; B = B^\top > 0$$ with $\lambda \approx \sigma$ using Rayleigh Quotient Iteration (RQI) (RQI is ...
1
vote
1answer
45 views

Algorithms for one-to-many assignment problem

I'm looking for a computationally efficient algorithm for solving the following type of assignment problem: I have two sets of points. Set A has N points and set B has M points. I'd like to establish ...
0
votes
0answers
11 views

Fine grained control over NGen-IC [closed]

Is it possible to specify the initial positions and velocities of particles so that NGen IC uses such a file and creates a Gadget-2 compatible file ?
1
vote
1answer
70 views

I need to scale variables to solve a 2D PDE. What are the physical considerations of scaling?

I am solving a boundary value problem in 2D via an implicit finite difference scheme. Unfortunately, although the problem is well-posed and should have a unique solution, the condition number of the ...
3
votes
2answers
108 views

How to Run MPI-3.0 in shared memory mode like OpenMP

I am parallelizing code to numerically solve a 5 Dimensional population balance model. Currently I have a very good MPICH2 parallelized code in FORTRAN but as we increase parameter values the arrays ...
1
vote
0answers
40 views

Computation of plane wave scattering on semi infinite plane

I have attempted to code up the simple math required to plot the total field set up by an incident plane wave on a semi-infinite flat plate which can be found here. To summarise: $$\phi_s(r,\theta ) ...
3
votes
1answer
24 views

Use scipy to get any vertex of polytope

I need to get just a random vertex of a polytope. Any will do. The only way I can do this now is to pick a random function (say 0s) to maximize with scipy.optimize.linprog. However, this is wasteful, ...
2
votes
0answers
37 views

Inverted value is not consistent with expectation

We have a group of observations $$y = f(x_1, x_2, x_3) \enspace .$$ We have also a forward model $y = f(x_1, x_2)$. The forward model does not include $x_3$ because $x_3$ might include dozens of ...

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