Nonlinear Time-Domain Finite Element Solver for Quantum Inforamtion Science Applications*

SLAC has developed the parallel finite element electromagnetics simulation suite ACE3P which employs the parallel high-order finite element (FE) method to solve Maxwell's equations at the macroscopic level. Under the support of an SLAC LDRD, optical nonlinearities in the transient regime have been incorporated into the ACE3P time-domain solver for the investigation of nonlinear physical processes such as harmonic generation, parametric processes and electro-optic effects. In a crystalline medium, a point group symmetry of the crystal dictates the type of nonlinear response to the applied field. The general case with both nonlinear χ⁽²⁾and χ⁽³⁾ susceptibilities in Maxwell's equations has been implemented through the weak formulation of the finite element method in ACE3P for 3D geometries. We have implemented data structures in the time-domain t3p code to account for nonlinear materials. This allows us to include χ⁽²⁾ and χ⁽³⁾ materials in arbitrary 3D geometries, in addition to the main constitutive parameters of the medium.  The new solver has been benchmarked against the commercial solver ANSYS Lumerical. The iterative solver has shown very good performance and strong scaling versus the number of cores used in the simulation.  As the nonlinear material susceptibilities introduce a dependence on the unknown variables, we are implementing additional code and data structures required for nonlinear methods. This includes the efficient handling of matrix updates and building Jacobian operators for sparse matrices for nonlinear methods.  Furthermore, we have completed the first prototype of the new nonlinear solver employing PETSc, a powerful suite of data-structure-neutral scalable numerical routines for large-scale linear and nonlinear problems. The PETSc library and the Scalable Nonlinear Equations Solvers (SNES) components include backend CPU and GPU implementation of its numerical solvers thus offering the needed numerical methods for solving Maxwell’s equations with nonlinearities. We expect this solver to be completed with the preliminary LDRD support while more support will be needed to overhaul the legacy ACE3P solver to allow better scalability and portability for the code for use by the community.