135 citations · 187 across the 14 of their papers we have counts for
14 papers
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…
Physics guided machine learning using simplified theories
Suraj Pawar, Omer San, Burak Aksoylu +2
Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences…
Incorporating local boundary conditions into nonlocal theories
Burak Aksoylu, Horst Reinhard Beyer, Fatih Celiker
We study nonlocal equations from the area of peridynamics on bounded domains. In our companion paper, we discover that, on , the governing operator in peridynamics, w…
On a Class of Nonlocal Wave Equations from Applications
Horst Reinhard Beyer, Burak Aksoylu, Fatih Celiker
We study equations from the area of peridynamics, which is an extension of elasticity. The governing equations form a system of nonlocal wave equations. Its governing operator is f…
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…