145 citations · 389 across the 30 of their papers we have counts for
8 papers · 1 filter
Allocation strategies for high fidelity models in the multifidelity regime
Daniel J. Perry, Robert M. Kirby, Akil Narayan +1
We propose a novel approach to allocating resources for expensive simulations of high fidelity models when used in a multifidelity framework. Allocation decisions that distribute c…
Combined CG-HDG Method for Elliptic Problems: Performance Model
Martin Vymazal, David Moxey, Chris Cantwell +2
We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors…
Parametric Topology Optimization with Multi-Resolution Finite Element Models
Vahid Keshavarzzadeh, Robert M. Kirby, Akil Narayan
We present a methodical procedure for topology optimization under uncertainty with multi-resolution finite element models. We use our framework in a bi-fidelity setting where a coa…
Generation of Nested Quadrature Rules for Generic Weight Functions via Numerical Optimization: Application to Sparse Grids
Vahid Keshavarzzadeh, Robert M. Kirby, Akil Narayan
We present a numerical framework for computing nested quadrature rules for various weight functions. The well-known Kronrod method extends the Gauss-Legendre quadrature by adding n…
RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for Solving PDEs on Surfaces
Varun Shankar, Akil Narayan, Robert M. Kirby
We present a new method for the solution of PDEs on manifolds of co-dimension one using stable scale-free radial basis function (RBF) interpolatio…
Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces
Varun Shankar, Robert M. Kirby, Aaron L. Fogelson
We present a new algorithm for the automatic one-shot generation of scattered node sets on irregular 2D and 3D domains using Poisson disk sampling coupled to novel parameter-free,…
Numerical Integration in Multiple Dimensions with Designed Quadrature
Vahid Keshavarzzadeh, Robert M. Kirby, Akil Narayan
We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enf…
Curvilinear Mesh Adaptation using Radial Basis Function Interpolation and Smoothing
Vidhi Zala, Varun Shankar, Shankar P. Sastry +1
We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or…