For questions on methods for solving partial differential equations by decomposition of a continuous or discrete operator into two or more separate operators.

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2
votes
0answers
92 views

Segregated solving of a tightly coupled system of PDEs

To compute the evolution of a free surface between two incompressible, immiscible liquids, two tightly coupled equations have to be solved, the volume fraction advection and the Navier-Stokes ...
1
vote
0answers
126 views

Derivation of a Higher Order Compact Alternating Direction Implicit Method

I dont understand how this Higher Order Compact ADI scheme, which is fourth order in time and space, for the wave equation is derived: I go through the following Using Tylor's expansion $u(t+h,x,y)$ ...
7
votes
0answers
163 views

Operator Splitting methods for non-standard forms

After doing some research, I've found that most of the literature on operator splitting methods (e.g. Strang Splitting, Fractional Step, etc.) are specifically designed for a standard problem type of ...
3
votes
1answer
108 views

Iterative Block Matrix Splitting for Multiphysics Simulation

I have a problem of the form $$\left[\begin{array}{cc} -(\lambda+2\mu)\frac{d^2}{dx^2} & \alpha\frac{d}{dx} \\ \frac{\alpha}{\Delta t}\frac{d}{dx} & \frac{c_0}{\Delta ...
9
votes
1answer
488 views

Optimal use of Strang splitting (for reaction diffusion equation)

I made a strange observation while computing the solution to a simple 1D reaction diffusion equation: $\frac{\partial}{\partial t}a=\frac{\partial^2}{\partial x^2}a-ab$ ...
11
votes
4answers
327 views

Are there operator splitting approaches for multiphysics PDEs that achieve high order convergence?

Given an evolution PDE $$u_t = Au + Bu$$ where $A,B$ are (possibly nonlinear) differential operators that don't commute, a common numerical approach is to alternate between solving $$u_t = Au$$ ...