135 citations · 187 across the 14 of their papers we have counts for
7 papers · 1 filter
Coupling of Local and Nonlocal Problems Using Local Boundary Conditions
Burak Aksoylu, Fatih Celiker, Patrick Diehl
We present a novel coupling method for local and nonlocal diffusion problems in 1D. Unlike other methods, our coupling method exclusively uses local boundary conditions. This is po…
Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation
Burak Aksoylu, Stephen Bond, Eric Cyr +1
In this article, we develop goal-oriented error indicators to drive adaptive refinement algorithms for the Poisson-Boltzmann equation. Empirical results for the solvation free ener…
Local Refinement and Multilevel Preconditioning: Implementation and Numerical Experiments
Burak Aksoylu, Stephen Bond, Michael Holst
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While st…
Optimality of multilevel preconditioners for local mesh refinement in three dimensions
Burak Aksoylu, Michael Holst
In this article, we establish optimality of the Bramble-Pasciak-Xu (BPX) norm equivalence and optimality of the wavelet modified (or stabilized) hierarchical basis (WHB) preconditi…
Robust multigrid preconditioners for the high-contrast biharmonic plate equation
Burak Aksoylu, Zuhal Yeter
We study the high-contrast biharmonic plate equation with HCT and Morley discretizations. We construct a preconditioner that is robust with respect to contrast size and mesh size s…
Variational Theory and Domain Decomposition for Nonlocal Problems
Burak Aksoylu, Michael L. Parks
In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish…