0
votes
0answers
7 views

Realistic expression to induce a seismic wave in 2D/ 3D fem mesh?

I have a 2D square mesh and a 3D beam shaped mesh and I want to propagate a seismic wave in them. I am trying to simulate them using Open source FEM codes (fenics). I have left the top surface to be ...
1
vote
1answer
27 views

A fast I/O file format readable by Fortran, Java, PHP?

I am writing a Fortran program that does fairly light weigt computation on fairly large data files. The output must be readable by some Java-script (that i have no insight in) and preferably also by ...
0
votes
0answers
18 views

Reaction-diffusion equations

I'm simulating a biological phenomena with reaction diffusion equations. There are multiple diffusing materials and there are some complex relations about consumption and production of such materials. ...
0
votes
0answers
15 views

Matlab PDE toolbox problems specifying geometry with large size differences

I am trying to solve an elliptic PDE using MATLAB's PDE toolbox. I am trying to solve the problem on an annulus where the inner radius (r_0) is significantly smaller than the outer radius (R.) ...
0
votes
0answers
30 views

Exact finite difference method for advection equation

I want to solve the advection equation: $u_t+au_x=0, a > 0$. Here is our method: $$U_j^{n+1}=U_{j-1}^n-\left(\frac{ak}{h}-1\right)(U_{j-1}^n - U_{j-2}^n)$$ I am trying to answer the following ...
0
votes
1answer
21 views

hyperbolic equation and characteristics

I am a little confused about the connection between variables for the plain advection pde: $$u_t+au_x=0$$ So initially I thought $x$ and $t$ are independent and $u$ is a function of those, but then we ...
1
vote
1answer
17 views

Implicit projection method with inflow boundary conditions

I am trying to use a projection method that deals with the viscous effects implicitly to model flow around a cylinder. I'm having trouble figuring out what the boundary conditions should be, ...
0
votes
0answers
36 views

Weak form for elastoplastic wave propagation

I am trying to simulate elastoplastic seismic wave propagation using Fenics Solid Mechanics Application. The app. provides some quasi-static demos to show elastoplastic behaviour in a cube/ beam/ ...
1
vote
0answers
23 views

How to impose boundary conditions for higher order derivatives in eigenvalue problems?

The following boundary value problem $y'''' + r \, y'' = 0$ with the boundary conditions $y'' =y'''=0$ at both ends is a generalised eigenvalue problem of the kind \begin{equation} M\,x = \lambda \, ...
1
vote
0answers
10 views

How to calculate multi-class prediction probabilities using One vs All and One vs One classifiers

To be specific, let's consider Support Vector Machines. In the 1 vs all case, one has $n$ binary classifiers where $n$ is the number of classes. In each classifier one has two labels 0, 1 and for a ...
4
votes
0answers
81 views

Effects of Lumping Mass Matrix

I've recently finished an introductory course on the finite element method from a more mathematical perspective (following Brenner and Scott) and we were introduced to the finite element mass matrix ...
3
votes
1answer
44 views

Can singularity screw up your model?

I've been running some complicated Finite Element Models. In most cases, the stress repartition seemed to be absolutely correct. However, on several point (complicated geometry), it appears that ...
1
vote
0answers
20 views

Inner Products vs Discretizations of Functions

Let $f:(0,1)\rightarrow [0,1]$ be a $\mathcal{C}^{\infty}$ function. We say that a function $D_r^f:\{1,...,r\}\rightarrow [0,1]$ is an $r$-discretization of $f$ if $$D_r^f(j) = \frac{1}{|a(j)-b(j)|}\...
0
votes
0answers
8 views

How does one advect fluids in the Simple Line interface Calculation algorithm (SLIC)?

SLIC is an algorithm to track the interface between two or more immiscible fluids in a simulation. When one reads the paper, we see that it explains how to define the interface between fluids but not ...
4
votes
1answer
59 views

Space-time Galerkin of Burgers changes the convection speed

tldr: Can space-time Galerkin schemes applied to convection-diffusion problems lead to effects on the convection velocity? For time $t\in (0,1)$ and the spatial variable $\xi \in (0,1)$, I am ...
0
votes
0answers
14 views

Are Tecplot's streamtraces different from streamlines? [on hold]

In Tecplot, there is option to plot streamtraces. Are these same as streamlines. If yes, why is it names streamtraces and not streamlines. Is there any difference between the two.
4
votes
1answer
63 views

Motivation behind Collocation Method

In previous question "Motivation behind Galerkin method", Paul gives a good and easy-understanding explanation indicating that the Galerkin method is a kind of projection method. Can anyone explain ...
3
votes
0answers
25 views

Sparse matrix format and sparse-matrix sparse-matrix multiplication

Good morning, I'm having some performance problems with my code dealing with the multiplication of big sparse matrices (stiffness and aerodynamic influence coefficient matrices). Mainly I have to ...
0
votes
1answer
43 views

Solving Time dependent Schrodinger equation using MATLAB ode45

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ I try to implement solve the Schrodinger equation for time-dependent Hamiltonian in ODE ...
7
votes
3answers
112 views

What does Python offer for distributed/parallel/GPU computing?

Using the SciPy/NumPy libraries, Python is a pretty cool and performing platform for scientific computing. I just wonder: When I have to go parallel (multi-thread, multi-core, multi-node, gpu), what ...
3
votes
0answers
23 views

Defining Cauchy principal value in MATLAB (or Scilab/Maple)?

How to define a variable which is an integral involving cauchy principal value inside in any computer programming language? I want to know how to break down the procedure step by step from a ...
0
votes
1answer
35 views

Implementing velocity verlet for harmonic oscillator in C gives error wrt conservation of energy

I'm attempting to implement velocity Verlet with a harmonic oscillator in C, but I have some errors: Energy is not being conserved Energy oscillates much more than I would expect I believe the ...
4
votes
2answers
72 views

Finding quick solution to a collection of systems of fairly simple but nonlinear equations

So I have a collection of systems of equations, basically $n$ systems of equations, each composed of $k$ equations: $$\frac{a_1x_{1j}}{a_1x_{1j} + \cdots + a_kx_{kj}} + \log x_{1j} + 1 - B_{1j} = 0$$ ...
4
votes
1answer
46 views

numerical approach for system of non-linear partial-ordinary differential equations

I am interested in the numerical solution of the following system of non-linear partial-differential algebraic equations, where the independent variables are $X$ and $T$, representing non-dimensional ...
1
vote
1answer
65 views

How is the mass matrix formed in finite element methods?

as i am doing project on mass matrix, i want to know how to develop mass matrix. so please explain me how to develop mass matrix in detail.
1
vote
0answers
27 views

Implicit equation solving COMSOL [closed]

I want to solve a implicit equation in a domain in 1-D geometry. The equation looks like this: i=exp(phi1-phi2-U-i*R) phi1,phi2 are time and space dependent variables. R is a constant. I tried ...
1
vote
2answers
30 views

How are the outcomes that generated from different predictive models combined to get more accurate predictions?

The simple average is commonly used to combine the predictions out of different predictive models. Apart form the simple average, what are the other methods that can be used for combining the ...
5
votes
1answer
69 views

Finite element error for second order ODE at nodes equal to zero

I coded a finite element method with linear basis elements for the problem $$-u'' = f(x), x\in[0,1], u(0) = u(1) = 0$$ The nodes are uniformly spaced and I will denote them as $x_i$. I initially ...
0
votes
0answers
15 views

acessing BOXLIB librrarry in ubuntu [closed]

i am new for Ubuntu,i installed boxlib library which is found in Ubuntu software center but i can't access. it so what shall i do?is there any steps i have to follow and installed may be like GNU make?...
0
votes
1answer
60 views

Hyperscale Vs Strong-scale HPC

NVIDIA's Tesla GPUs for Servers includes market segments called "Hyperscale HPC" and "Strong-Scale HPC". How different is ...
0
votes
0answers
95 views

Unknown function

This is my first question. I have the following data that I'd like to express as a function: Any suggestions how to modify the function shown below so as to get a closer fit?
1
vote
0answers
62 views

Choose of basis set

I am engaged with the syntheses and DFT calculations of coordination complexes. I wonder how can I set up the basis set for carried out using B3LYP method and mixed basis sets of LanL2DZ for Pd and 6-...
0
votes
1answer
124 views

Fortran round-off error with floating point operations

I have simple code, which flags nodes with in region enclosed by cylinder. On implementing the code, the result is mild tilt of the cylinder observed case with $\theta=90^{\circ}$. The algorithm for ...
0
votes
0answers
29 views

Stiff ODEs coupled with PDEs (computational efficiency)

I am simulating in COMSOL a system of 3 coupled PDEs (parabolic & elliptic) along with 10 stiff ODEs. In order to have the system working, I am downsizing the time step size too much to achieve ...
4
votes
2answers
77 views

How should I set the velocity conditions when you have a pressure inlet and pressure outlet?

I know that when modeling incompressible flow in a pipe, it is common practice that when you have a velocity inlet, there should be a zero pressure gradient at the inlet as well. Also, when you have ...
1
vote
0answers
38 views

Pressure boundary condition in Navier-Stokes equations

I would like to solve 3D transient incompressible Navier-Stokes with FEM, Newton method, Schur-based preconditioner, Lagrangean P2/P1 elements (no stabilization), in a rigid pipe discretized with ...
0
votes
1answer
24 views

Existing Solver for large scale load dependent Ritz vectors problem

I have a large scale system with the following equations of motions $M\ddot z(t)+K z(t)=F(t)$ $M$ is the mass matrix $K$ is the stiffness matrix And I want to solve the equation for displacement $...
0
votes
1answer
39 views

Show the symmetric Gauss-Seidel converges for any $x_0$

Let $A\in\mathbb{R}^{n\times n}$ is symmetric positive definite and consider solving linear system $Ax = b$. Show that the symmetric Gauss-Seidel iteration converges for any $x_0$. Solution - Since $...
0
votes
1answer
35 views

Running a script that asks for user input from a pbs file

I am trying to run a pbs file which runs a script on a cluster. The script prompts for a user input. I wish to write this user input in my pbs file, what is a good way to do this?
0
votes
0answers
14 views

How Many Edges can be in a K-regular Hypergraph?

In a Hypergraph k-regular ,with a set of n vertex , $V=\{v_{1},v_{2},...,v_{n}\}$ , how many edges can be at most in the hypergraph? similar to say that in a undirect graph of n vertex can be at most $...
-1
votes
0answers
20 views

One iteration of forward Gauss-Seidel followed by one iteration of backward Gauss-Seidel

Let $A = D - L - U\in\mathbb{R}^{n\times n}$ be a nonsingular matrix, where $-L$ is the matrix of strictly lower triangular elements and $-U$ is the matrix of strictly upper triangular elements. ...
0
votes
0answers
23 views

Solving nonlinear coupled PDE using FiPy

I have recently been trying to solve these 6 coupled, nonlinear PDEs of the general form: $ \frac {\partial N_1}{\partial t} = -a(P_2E_1 + P_1E_2) - bN_1 \\ \frac {\partial N_2}{\partial t} = -c ...
3
votes
1answer
73 views

Comparison of velocity Verlet and leapfrog algorithms

Many sources present the Euler, Verlet, velocity Verlet, and leapfrog algorithms for integrating Newton's equations. Based on the order of accuracy, it is agreed that velocity Verlet, Verlet, and ...
0
votes
0answers
41 views

If $A = I - P$ where $P\geq 0$ and $\rho(P)<1$ then $A$ is an $M$-matrix

Prove that if $A$ can be written as $A = I - P$ where $P\geq 0$ and $\rho(P) < 1$ then $A$ is an $M$-matrix Attempted proof - Suppose $A$ can be written as $A = I - P$ where $P\geq 0$ and $\rho(P)...
3
votes
1answer
94 views

Solve an ODE with positivity-preserving property unconditionally

I have an ODE for a scalar function $u=u(t)$ of the form: $$ \frac{du}{dt}=L(u). $$ Here the function $L=L(u)$ satisfies: $$ L(0)=0, \quad L'(u)\le0. $$ Then it is easy to see that the solution $u=u(t)...
0
votes
0answers
29 views

How to optimize interaction of flexible 3D shapes in space/what is this technique called

I am not sure what terminology I should use here or even what field this is. That information itself would be incredibly helpful, this is new territory for me. I'm trying to figure out how to solve ...
2
votes
1answer
51 views

How does Multi Body Dynamics software work for flexible joints?

I need to model a "fishing rod" in 2 dimensions by joining several "rigid sticks" by flexible/elastic joints. The joints act as plate/torsion springs with different spring constants. The "fishing rod" ...
0
votes
1answer
64 views

Linear stationary iteration method

Suppose you are attempting to solve $Ax = b$ using linear stationary iteration method defined by $$x_k = G x_{k-1} + f$$ that is consistent with $Ax = b$, i.e., for which $f = (I - G)A^{-1}b$. Suppose ...

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