85 citations · 289 across the 25 of their papers we have counts for
28 papers
Conforming Finite Element Function Spaces in Four Dimensions, Part II: The Pentatope and Tetrahedral Prism
David M. Williams, Nilima Nigam
In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope and tetrahedral prism element…
Conforming Finite Element Function Spaces in Four Dimensions, Part 1: Foundational Principles and the Tesseract
Nilima Nigam, David M. Williams
The stability, robustness, accuracy, and efficiency of space-time finite element methods crucially depend on the choice of approximation spaces for test and trial functions. This i…
Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: a numerical study
Javier A. Almonacid, Nilima Nigam
The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors".…
A Steklov-spectral approach for solutions of Dirichlet and Robin boundary value problems
Kthim Imeri, Nilima Nigam
In this paper we revisit an approach pioneered by Auchmuty to approximate solutions of the Laplace- Robin boundary value problem. We demonstrate the efficacy of this approach on a…
A three-dimensional model of skeletal muscle tissues
Javier A. Almonacid, Sebastián A. Domínguez-Rivera, Ryan N. Konno +4
Skeletal muscles are living tissues that can undergo large deformations in short periods of time and that can be activated to produce force. In this paper we use the principles of…
A simple extrapolation method for clustered eigenvalues
Nilima Nigam, Sara Pollock
This paper introduces a simple variant of the power method. It is shown analytically and numerically to accelerate convergence to the dominant eigenvalue/eigenvector pair; and, it…
The energy of muscle contraction. II. Transverse compression and work
D. S. Ryan, S. Domínguez, S. A. Ross +2
In this study we reproduced this compression-induced reduction in muscle force through the use of a three-dimensional finite element model of contracting muscle. The model used the…
The energy of muscle contraction. I. Tissue force and deformation during isometric contractions
J. M. Wakeling, S. A. Ross, D. S. Ryan +4
During contraction the energy of muscle tissue increases due to energy from the hydrolysis of ATP. This energy is distributed across the tissue as strain-energy potentials in the c…
Korn's inequality and Jones eigenpairs
Sebastián Domínguez, Nilima Nigam
In this paper we show that Korn's inequality \cite{ref:korn1906} holds for vector fields with a zero normal or tangential trace on a subset (of positive measure) of the boundary of…
Wave Enhancement through Optimization of Boundary Conditions
Habib Ammari, Oscar Bruno, Kthim Imeri +1
It is well known that changing boundary conditions for the Laplacian from Dirichlet to Neumann can result in significant changes to the associated eigenmodes, while keeping the eig…
Optimization of Steklov-Neumann eigenvalues
Habib Ammari, Kthim Imeri, Nilima Nigam
This paper examines the Laplace equation with mixed boundary conditions, the Neumann and Steklov boundary conditions. This models a container with holes in it, like a pond filled w…
Revisiting the Jones eigenproblem in fluid-structure interaction
Sebastián Domínguez, Nilima Nigam, Jiguang Sun
The Jones eigenvalue problem first described by D.S. Jones in 1983 concerns unusual modes in bounded elastic bodies: time-harmonic displacements whose tractions and normal componen…
Well-posed Bayesian Inverse Problems: Priors with Exponential Tails
Bamdad Hosseini, Nilima Nigam
We consider the well-posedness of Bayesian inverse problems when the prior measure has exponential tails. In particular, we consider the class of convex (log-concave) probability m…
Nearly radial Neumann eigenfunctions on symmetric domains
Nilima Nigam, Bartłomiej Siudeja, Benjamin Young
We study the existence of Neumann eigenfunctions which do not change sign on the boundary of some special domains. We show that eigenfunctions which are strictly positive on the bo…
Structural Changes of Active Skeletal Muscles: Modelling, Validation and Numerical Experiments
Hadi Rahemi, Nilima Nigam, James M. Wakeling
The purpose of this study was to report numerical validation of a 3D finite element model of contracting muscle. The model was based on continuum theory for fibre-reinforced compos…
On regularizations of the delta distribution
Bamdad Hosseini, Nilima Nigam, John M. Stockie
In this article we consider regularizations of the Dirac delta distribution with applications to prototypical elliptic and hyperbolic partial differential equations (PDEs). We stud…
A boundary integral algorithm for the Laplace Dirichlet-Neumann mixed eigenvalue problem
Eldar Akhmetgaliyev, Oscar Bruno, Nilima Nigam
We present a novel integral-equation algorithm for evaluation of Zaremba eigenvalues and eigenfunctions}, that is, eigenvalues and eigenfunctions of the Laplace operator with mixed…
Integral equation methods for the Yukawa-Beltrami equation on the sphere
Nilima Nigam, Mary-Catherine Kropinski, Bryan Quaife
An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Bel…
Fast integral equation methods for the Laplace-Beltrami equation on the sphere
Mary Catherine A. Kropinski, Nilima Nigam
Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mappe…
Convergence analysis of a multigrid algorithm for the acoustic single layer equation
Simon Gemmrich, Jay Gopalakrishnan, Nilima Nigam
We present and analyze a multigrid algorithm for the acoustic single layer equation in two dimensions. The boundary element formulation of the equation is based on piecewise consta…
Geometric integration on spheres and some interesting applications
Debra Lewis, Nilima Nigam
Geometric integration theory can be employed when numerically solving ODEs or PDEs with constraints. In this paper, we present several one-step algorithms of various orders for ODE…
Boundary Integral Equations for the Laplace-Beltrami Operator
Simon Gemmrich, Nilima Nigam, Olaf Steinbach
We present a boundary integral method, and an accompanying boundary element discretization, for solving boundary-value problems for the Laplace-Beltrami operator on the surface of…
The cellular dynamics of bone remodeling: a mathematical model
Marc Ryser, Svetlana V. Komarova, Nilima Nigam
The mechanical properties of vertebrate bone are largely determined by a process which involves the complex interplay of three different cell types. This process is called {\it bon…
On the well-posedness of the stochastic Allen-Cahn equation in two dimensions
Marc D. Ryser, Nilima Nigam, Paul F. Tupper
White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d…