For questions on methods for solving partial differential equations by decomposition of a continuous or discrete operator into two or more separate operators.
3
votes
1answer
77 views
Iterative Block Matrix Splitting for Multiphysics Simulation
I have a problem of the form
$$\left[\begin{array}{cc}
-(\lambda+2\mu)\frac{d^2}{dx^2} & \alpha\frac{d}{dx} \\
\frac{\alpha}{\Delta t}\frac{d}{dx} & \frac{c_0}{\Delta ...
6
votes
0answers
250 views
Optimal use of Strang splitting (for reaction diffusion equation)
I made a strange observation while computing the solution to a simple 1D reaction diffusion equation:
$\frac{\partial}{\partial t}a=\frac{\partial^2}{\partial x^2}a-ab$
...
10
votes
4answers
239 views
Are there operator splitting approaches for multiphysics PDEs that achieve high order convergence?
Given an evolution PDE
$$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$$
...
