Questions tagged [time-integration]

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Conservation of energy test for 2-body problem

I'm trying to implement a C++ code for the evaluation of the solution of an N-body system of ODE. I've started with a 2-body problem just to set the methods ...
110 views

Second Order Time Integration for Stiff Linear System Avoiding any Explicit Step

I have a linear system $$\dot x(t) = Ax(t), \quad x(0)=x_0 \tag{*}$$ with $A$ being Hurwitz (i.e. the solutions may oscillate but will eventually tend to zero) but really stiff. $A$ might be large, ...
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Parallel In Time with Multigrid

I am trying to solve the linear finite element equation $M\ddot{u}+Ku=F(t)$, where $M$ is the mass matrix ,$K$ the stiffness matrix and $F(t)$ the external load vector, parallel in time using XBraid ...
83 views

Numerical integration in time for finite elements

I am trying to solve $M\ddot{u}=-Ku+F_\text{ext}$ for a 2D linear elastic model with $M$ be the mass matrix,$K$ the stiffness matrix and $F_\text{ext}$ the external load vector coming from a uniformly ...
137 views

How do I apply BDF2 in a STRANG splitting

I have a 3D diffusion equation that I want to solve using a time splitting (2D+1D). Assume that $A$ is the 2D discrete diffusion operator and $B$ is the 1D discrete diffusion operator. I want to use a ...
159 views

How to calculate the average velocity over a surface through time using paraview?

My problem is a little more complex, but here is a simplified similar model. Let us consider a fire source inside a box and the hot gases (burnt or unburnt) from the combustion are going out of the ...
151 views

Mass conservation for hyperbolic relaxation problem

I have solved numerically the following system: \begin{cases} \partial_t{u} + \partial_x{v} = 0 \\ \partial_t{v} + \frac{1}{\varepsilon^2}\partial_x{u} = -\frac{1}{\varepsilon^2}(v-f(u)) \end{cases} ...
512 views

The velocity Verlet method and variable time steps

Does the velocity Verlet handle variable time steps? I found controversial statements about it. In the paper Skeel, R. D., "Variable Step Size Destabilizes the Stömer/Leapfrog/Verlet Method", BIT ...
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Integrating the 2d vorticity equation on periodic boundaries

This question is a follow-up of https://stackoverflow.com/questions/44718160/solve-a-linear-system-for-fft-coefficients At some time (kt), the FT of the vorticity (omega) satisfies: ...
3k views

BDF vs implicit Runge Kutta time stepping

Are there any reasons for why one should choose high order implicit Runge Kutta (IMRK) over BDF time stepping? BDF seems much easier to me as $q$ stage IMRK needs $q$ linear solves per time step. ...
218 views

Fully discrete finite element method for 1D dynamic euler-bernoulli beam problem

I am trying to solve a 1D initial boundary value problem in MATLAB using Finite Elements with time stepping, for the purpose of learning scientific computing and to build up to more difficult problems....