Nathan Collier

The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements

In this paper we study how the use of a more continuous set of basis functions affects the cost of solving systems of linear equations resulting from a discretized Galerkin weak form. Specifically, we compare performance of linear solvers when discretizing using

An energy-stable convex splitting for the phase-field crystal equation

C^0

Phase field modeling using PetIGA

B-splines, which span traditional finite element spaces, and

A survey on direct solvers for Galerkin methods

C^{p-1}

Gradient-based estimation of Manning's friction coefficient from noisy data

B-splines, which represent maximum continuity. We provide theoretical estimates for the increase in cost of the matrix-vector product as well as for the construction and application of black-box preconditioners. We accompany these estimates with numerical results and study their sensitivity to various grid parameters such as element size

Time adaptivity in the diffusive wave approximation to the shallow water equations

h

Two-dimensional HP-adaptive Algorithm for Continuous Approximations of Material Data Using Space Projection

and polynomial order of approximation

Optimal multi-agent path planning for fast inverse modeling in UAV-based flood sensing applications

p

Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

. Finally, we present timing results for a range of preconditioning options for the Laplace problem. We conclude that the matrix-vector product operation is at most

On round-off error for adaptive finite element methods

\slfrac{33p^2}{8}