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A dissipative particle dynamics method for arbitrarily complex geometries
Zhen Li, Xin Bian, Yu-Hang Tang +1
We present a local detection method for dissipative particle dynamics (DPD) involving arbitrarily shaped geometric three-dimensional domains. By introducing an indicator variable o…
GPU-accelerated Red Blood Cells Simulations with Transport Dissipative Particle Dynamics
Ansel L. Blumers, Yu-Hang Tang, Zhen Li +2
Mesoscopic numerical simulations provide a unique approach for the quantification of the chemical influences on red blood cell functionalities. The transport Dissipative Particles…
A Petrov-Galerkin Spectral Element Method for Fractional Elliptic Problems
Ehsan Kharazmi, Mohsen Zayernouri, George Em Karniadakis
We develop a new -continuous Petrov-Galerkin spectral element method for one-dimensional fractional elliptic problems of the form ${}_{0}{\mathcal{D}}_{x}^α u(x) - λu(x) =…
Implicit-Explicit difference schemes for nonlinear fractional differential equations with non-smooth solutions
Wanrong Cao, Fanhai Zeng, Zhongqiang Zhang +1
We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order . From the known structure of th…
A Tunably-Accurate Laguerre Petrov-Galerkin Spectral Method for Multi-Term Fractional Differential Equations on the Half Line
Anna Lischke, Mohsen Zayernouri, George Em Karniadakis
We present a new tunably-accurate Laguerre Petrov-Galerkin spectral method for solving linear multi-term fractional initial value problems with derivative orders at most one and co…
Inferring solutions of differential equations using noisy multi-fidelity data
Maziar Raissi, Paris Perdikaris, George Em. Karniadakis
For more than two centuries, solutions of differential equations have been obtained either analytically or numerically based on typically well-behaved forcing and boundary conditio…