Questions tagged [operator-splitting]
For questions on methods for solving partial differential equations by decomposition of a continuous or discrete operator into two or more separate operators.
31
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Implicit-Explicit Operator Splitting Scheme
I am trying to solve the 2D advection-diffusion equation in cylindrical coordinates:
$$
\frac{\partial c}{\partial t} = D\left(\frac{\partial^2 c}{\partial r^2} + \frac{1}{r}\frac{\partial c}{\partial ...
- 11
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125
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Crank-Nicolson vs Spectral Methods for the TDSE
The time-dependent Schroedinger equation (TDSE) depends linearly on the system's initial state $\vert \psi(0) \rangle$, such that the solution can be generally written as
$$ \vert \psi(t) \rangle = \...
- 111
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schrodinger eq time propagation with dissipation using split step operator
I am looking in ways to include energy dissipation while propagating a coherent wavepacket in a 1d TDSE. for example I use the split step method: exp[Δt(D+V)]≈exp[ΔtV/2]exp[ΔtD]exp[ΔtV/2], and ...
- 121
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How does the error work for the Strang Splitting?
We know in Strang splitting that the splitting error in the steady state solution is proportional to $h^2$. I want ask 2 things:
If this error in the steady state solution is the global error?
If we ...
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163
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What is temporal order of accuracy of the PISO algorithm?
A few Computational Fluid Dynamics (CFD) codes implement the so called PISO (Pressure-Implicit with Splitting of Operators) algorithm for pressure-velocity coupling.
My concern is what is actual ...
- 1,403
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1
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223
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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 ...
- 53
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496
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Operator splitting to solve time dependent Schrödinger equation
I encountered the split operator method to solve the time dependent Schrödinger equation during a lecture. I understand the method on a theoretical basis (I think at least), but I'm struggling to ...
- 131
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Split-step Fourier method applied on Schrodinger equation
I'm trying to solve a Schrodinger equation of the form $i\frac{\partial}{\partial t}\psi=-\frac{\partial^2}{\partial x^2}\psi + (V(x)+\alpha|\psi|^2)\psi$ using the split-step Fourier method ...
- 21
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Should I expect computational gains using a second-order splitting method here?
I am trying to solve a three-dimensional baroclinic transport problem. The hydrodynamic (three-dimensional shallow water) equations are:
\begin{align}
\nabla \cdot \vec{v} = 0, \tag{1} \\
\frac{\...
- 389
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133
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General questions regarding stability for time-integration of operator-split PDE systems
I am interested in solving ODE systems of the form
\begin{align}
\frac{\partial \vec{u}}{\partial t} = F(\vec{u})
\end{align}
where $F$ is a nonlinear operator, $\vec{u}$ is a vector valued function ...
- 389
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2
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103
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Operator splitting for 4 subproblems
Typically an ODE System which involves 2 different physical problems such as diffusion and advection can be numerically approached by the well known Strang operator splitting scheme. I'm wondering if ...
- 146
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0
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163
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Split-step-method for coupled equations
I have implemented a split-step-method for an equation of the shape
$$\partial_z E = i\partial_x^2E+ic|E|^2E$$
resulting in a split into the linear part
$$L=\partial_x^2$$
and the nonlinear part
$$N=...
- 563
1
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0
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How to formulate Poisson's equation into flux eqution
I have a small 2D system I'm trying to model using a non-linear extension of Darcy's law for fluid flow in porous media. I'm primarily interested in the local flow velocity, not necessarily the ...
- 684
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142
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Stability of dark solitons in a harmonic trap
This question is based upon a research article which I am trying to reproduce. One of the main result of this paper is the condition on transverse confinement of the Bose-Einstein Condensate(BEC) to ...
- 135
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0
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Growing error from a smooth initial condition for Fisher KPP equation
I'm studying the Fisker-KPP equation on the line (and in $]0, 100[$ numerically):
$$
\partial_t u = \Delta_{xx} u + u(1-u)
$$
I notice a behavior I don't understand with a smooth initial condition $...
- 443