The Parabolic Synthesis methodology is an approximation methodology for implementing unary functions, such as trigonometric functions, logarithms and square root, as well as binary functions, such as division, in hardware.
We also provide a method for implementing an approximation of the regularized inversion of a SV-matrix, under the assumption of having smoothly spatially varying kernels, and enough regularization.
We also have proposed a method for implementing an approximation of the filtering of a SV-matrix regularized inverted, under the assumption of having smoothly varying kernels, and enough regularization.
Within the asymptotic framework, higher-order terms and the application of Padé approximation are implemented allowing for an extended applicability of asymptotic solutions.
A methodology for an inflow transport approximation is implemented in order to generate an accurate transport cross section.
A sequential optimization approach based on global conservative, convex and separable approximations is implemented for solving the optimization problem.
A fifth-order implicit Runge Kutta method and two fourth-order exponential integration methods equipped with Krylov subspace approximations were implemented for the GPU and paired with the analytical chemical kinetic Jacobian software pyJac.
Structural optimizations were done with the projector augmented wave potentials and the PBEsol45 generalized gradient approximation as implemented in the Vienna ab initio Simulation Package46,47.
Second-order PQL approximation, as implemented in MLwiN, was used.
In particular, the generalized gradient approximation, as implemented in the Vienna Ab Initio Simulation Package [20,21], was used to determine the phonon frequencies within the quasi-harmonic approximation.
