645 citations · 2.1k across the 59 of their papers we have counts for
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Label-free learning of elliptic partial differential equation solvers with generalizability across boundary value problems
Xiaoxuan Zhang, Krishna Garikipati
Traditional, numerical discretization-based solvers of partial differential equations (PDEs) are fundamentally agnostic to domains, boundary conditions and coefficients. In contras…
High Order Schemes for Gradient Flow with Respect to a Metric
Saem Han, Selim Esedoglu, Krishna Garikipati
New criteria for energy stability of multi-step, multi-stage, and mixed schemes are introduced in the context of evolution equations that arise as gradient flow with respect to a m…
A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method
Lampros Svolos, Hashem M. Mourad, Gianmarco Manzini +1
Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure u…
Reduced order models from computed states of physical systems using non-local calculus on finite weighted graphs
Matthew Duschenes, Krishna Garikipati
Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of phys…
High order, semi-implicit, energy stable schemes for gradient flows
Alexander Zaitzeff, Selim Esedoglu, Krishna Garikipati
We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possib…
Second Order Threshold Dynamics Schemes for Two Phase Motion by Mean Curvature
Alexander Zaitzeff, Selim Esedoglu, Krishna Garikipati
The threshold dynamics algorithm of Merriman, Bence, and Osher is only first order accurate in the two-phase setting. Its accuracy degrades further to half order in the multi-phase…