At Ignition Computing, we are developing the PreconNet Toolbox in order to speed up the solving of systems of linear equations of the form Ax=b. Solving such systems is at the core of many multi-physics simulations, and often is the computational bottleneck of the simulation. Speeding up this step would significantly reduce compute power needs.
One approach is to use preconditioned iterative solvers, and to update the previous preconditioner: instead of generating a new one, the previous preconditioner is altered based on the current linear system. How to do this is still underexplored in the case of grid refinements such as in the figure on the right. Could an updated preconditioner be worth the cost compared to a newly generated one?
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