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An Isoparametric Finite Element Method for Time-fractional Parabolic Equation on 2D Curved Domain
This paper provides an efficient numerical scheme for approximating the solution of the time-fractional parabolic equation on 2D curved domain. Here,...
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Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces
In this paper, we prove sharp isoperimetric inequalities for lower order eigenvalues of Neumann Laplacian on bounded domains in both compact and...
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Numerical Methods for Constructing Suboptimal Packings of Nonconvex Domains with Curved Boundary
AbstractWe study the problem of constructing some optimal packings of simply-connected nonconvex plane domains with a union of congruent circles. We...
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Low cardinality positive interior cubature on NURBS-shaped domains
In this paper we propose an algorithm that computes a low cardinality PI-type (Positive weights and Interior nodes) algebraic cubature rule of degree n ...
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Analysis of Defects and Harmonic Grid Generation in Domains with Angles and Cutouts
AbstractA survey of works concerning difficulties associated with harmonic grid generation in plane domains with angles and cutouts is given, and...
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Maximizing the Second Robin Eigenvalue of Simply Connected Curved Membranes
The second eigenvalue of the Robin Laplacian is shown to be maximal for a spherical cap among simply connected Jordan domains on the 2-sphere, for...
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Semi-implicit Finite-Difference Methods for Compressible Gas Dynamics with Curved Boundaries: A Ghost-Point Approach
We present a finite-difference numerical method to solve systems of hyperbolic conservation laws in domains with arbitrary shapes. The curved...
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A Virtual Element Method for the Wave Equation on Curved Edges in Two Dimensions
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave...
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Quadrature Domains for the Helmholtz Equation with Applications to Non-scattering Phenomena
In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called...
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Sharp Reverse Isoperimetric Inequalities in Nonpositively Curved Cones
We prove a pair of sharp reverse isoperimetric inequalities for domains in nonpositively curved surfaces: (1) metric disks centered at the vertex of...
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A Broken FEEC Framework for Electromagnetic Problems on Mapped Multipatch Domains
We present a framework for the structure-preserving approximation of partial differential equations on mapped multipatch domains, extending the...
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Homogenization of Semi-linear Optimal Control Problems on Oscillating Domains with Matrix Coefficients
In this article, we study the homogenization of optimal control problems subject to second-order semi-linear elliptic PDEs with matrix coefficients...
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Lord Rayleigh’s Conjecture for Vibrating Clamped Plates in Positively Curved Spaces
We affirmatively solve the analogue of Lord Rayleigh’s conjecture on Riemannian manifolds with positive Ricci curvature for any clamped plates in 2...
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Improved Upper Bounds for the Hot Spots Constant of Lipschitz Domains
The Hot Spots constant for bounded smooth domains was recently introduced by Steinerberger (
2021 ) as a means to control the global extrema of the... -
Propagation of curved folding: the folded annulus with multiple creases exists
In this paper we consider developable surfaces which are isometric to planar domains and which are piecewise differentiable, exhibiting folds along...
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Coercive second-kind boundary integral equations for the Laplace Dirichlet problem on Lipschitz domains
We present new second-kind integral-equation formulations of the interior and exterior Dirichlet problems for Laplace’s equation. The operators in...
