Angular Adaptivity in P⁰ Space and Reduced Tolerance Solves for Boltzmann Transport

Previously, we developed an adaptive method in angle that is based on solving in Haar wavelet space with a matrix-free multigrid for Boltzmann transport problems. This method scalably mapped to the underlying P⁰ space during every matrix-free matrix-vector product; however, the multigrid method itself was not scalable in the streaming limit. To tackle this, we recently built an iterative method based on using an Approximate Ideal Restriction multigrid with GMRES polynomials (AIRG) for Boltzmann transport that showed scalable work with uniform P⁰ angle in the streaming and scattering limits. This paper details the practical requirements of using this new iterative method with angular adaptivity. Hence, we modify our angular adaptivity to occur directly in P⁰ space rather than the Haar space. We then develop a modified stabilization term for our Finite Element Method that results in scalable growth in the number of nonzeros in the streaming operator with P⁰ adaptivity. We can therefore combine the use of this iterative method with P⁰ angular adaptivity to solve problems in both the scattering and the streaming limits, with close to fixed work and memory use.We also present a coarse-fine splitting for multigrid methods based on element agglomeration combined with angular adaptivity, which can produce a semicoarsening in the streaming limit without access to the matrix entries. The equivalence between our adapted P⁰ and Haar wavelet spaces also allows us to introduce a robust convergence test for our iterative method when using regular adaptivity. This allows the early termination of the solve in each adapt step, reducing the cost of producing an adapted angular discretization.