209 citations · 282 across the 11 of their papers we have counts for
11 papers
ML-based identification of the interface regions for coupling local and nonlocal models
Noujoud Nader, Patrick Diehl, Marta D'Elia +2
Local-nonlocal coupling approaches combine the computational efficiency of local models and the accuracy of nonlocal models. However, the coupling process is challenging, requiring…
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
Manuel Klar, Giacomo Capodaglio, Marta D'Elia +3
Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the mai…
Control of fractional diffusion problems via dynamic programming equations
Alessandro Alla, Marta D'Elia, Christian Glusa +1
We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this…
An asymptotically compatible coupling formulation for nonlocal interface problems with jumps
Christian Glusa, Marta D'Elia, Giacomo Capodaglio +2
We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak f…
Machine-learning of nonlocal kernels for anomalous subsurface transport from breakthrough curves
Xiao Xu, Marta D'Elia, Christian Glusa +1
Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models ha…
A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems
Xiao Xu, Christian Glusa, Marta D'Elia +1
We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem wher…
A fractional model for anomalous diffusion with increased variability. Analysis, algorithms and applications to interface problems
Marta D'Elia, Christian Glusa
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. I…
An optimization-based approach to parameter learning for fractional type nonlocal models
Olena Burkovska, Christian Glusa, Marta D'Elia
Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal si…
Numerical methods for nonlocal and fractional models
Marta D'Elia, Qiang Du, Christian Glusa +3
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swa…
Optimal control of a parabolic fractional PDE: analysis and discretization
Christian Glusa, Enrique Otarola
We consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constrain…
A priori error estimates for the optimal control of the integral fractional Laplacian
Marta D'Elia, Christian Glusa, Enrique Otarola
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, fi…