“Advanced time integration methods for large-scale stiff nonlinear systems of differential equations”

In recent years, exponential time integration methods have emerged as an efficient alternative to classical and standard time integrators for solving large stiff systems resulting from spatial semi-discretization of nonlinear PDEs. These methods are fully explicit but do not suffer from the stability restrictions that constrain classical time integrators. Additionally, these methods can take much larger time steps than other approaches while maintaining the same level of accuracy. Thus they can offer significant computational savings, particularly for large-scale stiff systems where no efficient preconditioner is available. In this talk, I will introduce exponential methods, and present my work in their derivation, analysis, and implementation.  I will then present recent results using our new methods on applications in visual computing (elastodynamic models) and in meteorology (numerical weather prediction models).