35 citations · 37 across the 9 of their papers we have counts for
11 papers
A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations
Biswajit Khara, Suresh Murugaiyan, Makrand Khanwale +1
The Galerkin finite element formulation of the incompressible Navier-Stokes equations presents two principal challenges: maintaining stable velocity-pressure coupling and controlli…
Proximal Galerkin for Phase Field Fracture
Miguel Castillón, Biswajit Khara, Jørgen S. Dokken +3
The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of…
A Semi-Implicit Variational Multiscale Formulation for the Incompressible Navier-Stokes Equations via Exact Adjoint Linearization
Biswajit Khara, Suresh Murugaiyan, Suriya Dhakshinamoorthy +3
A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier-Stokes equations. The convection term is linearized using an ext…
Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples
Biswajit Khara, Robert Dyja, Kumar Saurabh +2
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we ap…
Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization
Biswajit Khara, Kumar Saurabh, Robert Dyja +2
We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-squar…
Neural PDE Solvers for Irregular Domains
Biswajit Khara, Ethan Herron, Zhanhong Jiang +8
Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention. However, the large majority of neural PDE solvers only a…
NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs
Biswajit Khara, Aditya Balu, Ameya Joshi +4
We consider a mesh-based approach for training a neural network to produce field predictions of solutions to parametric partial differential equations (PDEs). This approach contras…
Differentiable Spline Approximations
Minsu Cho, Aditya Balu, Ameya Joshi +6
The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differen…
Distributed Multigrid Neural Solvers on Megavoxel Domains
Aditya Balu, Sergio Botelho, Biswajit Khara +6
We consider the distributed training of large-scale neural networks that serve as PDE solvers producing full field outputs. We specifically consider neural solvers for the generali…
Industrial scale large eddy simulations (LES) with adaptive octree meshes using immersogeometric analysis
Kumar Saurabh, Boshun Gao, Milinda Fernando +7
We present a variant of the immersed boundary method integrated with octree meshes for highly efficient and accurate Large-Eddy Simulations (LES) of flows around complex geometries…
Deep Generative Models that Solve PDEs: Distributed Computing for Training Large Data-Free Models
Sergio Botelho, Ameya Joshi, Biswajit Khara +4
Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equation…