145 citations · 389 across the 30 of their papers we have counts for
32 papers
Particle Merging-and-Splitting
Nghia Truong, Cem Yuksel, Chakrit Watcharopas +2
Robustly handling collisions between individual particles in a large particle-based simulation has been a challenging problem. We introduce particle merging-and-splitting, a simple…
Structure-preserving Nonlinear Filtering for Continuous and Discontinuous Galerkin Spectral/hp Element Methods
Vidhi Zala, Robert M. Kirby, Akil Narayan
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized…
Towards an Extrinsic, CG-XFEM Approach Based on Hierarchical Enrichments for Modeling Progressive Fracture
M. Keith Ballard, Roman Amici, Varun Shankar +3
We propose an extrinsic, continuous-Galerkin (CG), extended finite element method (XFEM) that generalizes the work of Hansbo and Hansbo to allow multiple Heaviside enrichments with…
Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulations
Wei W. Xing, Akeel A. Shah, Peng Wang +2
Challenges in multi-fidelity modeling relate to accuracy, uncertainty estimation and high-dimensionality. A novel additive structure is introduced in which the highest fidelity sol…
A bandit-learning approach to multifidelity approximation
Yiming Xu, Vahid Keshavarzzadeh, Robert M. Kirby +1
Multifidelity approximation is an important technique in scientific computation and simulation. In this paper, we introduce a bandit-learning approach for leveraging data of varyin…
Fast Barycentric-Based Evaluation Over Spectral/hp Elements
Edward Laughton, Vidhi Zala, Akil Narayan +2
As the use of spectral/ element methods, and high-order finite element methods in general, continues to spread, community efforts to create efficient, optimized algorithms asso…
Kernel optimization for Low-Rank Multi-Fidelity Algorithms
Mani Razi, Robert M. Kirby, Akil Narayan
One of the major challenges for low-rank multi-fidelity (MF) approaches is the assumption that low-fidelity (LF) and high-fidelity (HF) models admit "similar" low-rank kernel repre…
Visualization of topology optimization designs with representative subset selection
Daniel J Perry, Vahid Keshavarzzadeh, Shireen Y Elhabian +3
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as i…
Deep Multi-Fidelity Active Learning of High-dimensional Outputs
Shibo Li, Robert M. Kirby, Shandian Zhe
Many applications, such as in physical simulation and engineering design, demand we estimate functions with high-dimensional outputs. The training examples can be collected with di…
Numerical Testing of a New Positivity-Preserving Interpolation Algorithm
T. A. J. Ouermi, Robert M. Kirby, Martin Berzins
An important component of a number of computational modeling algorithms is an interpolation method that preserves the positivity of the function being interpolated. This report des…
Structure-preserving function approximation via convex optimization
Vidhi Zala, Robert M. Kirby, Akil Narayan
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial a…
Multi-Fidelity High-Order Gaussian Processes for Physical Simulation
Zheng Wang, Wei Xing, Robert Kirby +1
The key task of physical simulation is to solve partial differential equations (PDEs) on discretized domains, which is known to be costly. In particular, high-fidelity solutions ar…
A Scalable Framework for Solving Fractional Diffusion Equations
Max Carlson, Robert M. Kirby, Hari Sundar
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there…
Deep Coregionalization for the Emulation of Spatial-Temporal Fields
Wei Xing, Robert M. Kirby, Shandian Zhe
Data-driven surrogate models are widely used for applications such as design optimization and uncertainty quantification, where repeated evaluations of an expensive simulator are r…
The Effect of Data Transformations on Scalar Field Topological Analysis of High-Order FEM Solutions
Ashok Jallepalli, Joshua A. Levine, Robert M. Kirby
High-order finite element methods (HO-FEM) are gaining popularity in the simulation community due to their success in solving complex flow dynamics. There is an increasing need to…
Nektar++: enhancing the capability and application of high-fidelity spectral/ element methods
David Moxey, Chris D. Cantwell, Yan Bao +14
Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the hi…
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…