Related papers: Regularized Stokeslet Surfaces
A general regularization strategy is considered for the efficient iterative solution of the lowest-order weak Galerkin approximation of singular Stokes problems. The strategy adds a rank-one regularization term to the zero (2,2) block of…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
LSQR, a Lanczos bidiagonalization based Krylov subspace iterative method, and its mathematically equivalent CGLS applied to normal equations system, are commonly used for large-scale discrete ill-posed problems. It is well known that LSQR…
Recent developments for mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling. In our former work, we have…
Motivated by applications in geomorphology, the aim of this paper is to extend Morse-Smale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3-dimensional…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
In dynamic MRI, sufficient time resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based image…
A triangular plate-bending element with a new multi-resolution analysis (MRA) is proposed and a novel multiresolution element method is hence presented. The MRA framework is formulated out of a displacement subspace sequence whose basis…
Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…
Prior knowledge on properties of a target model often come as discrete or combinatorial descriptions. This work provides a unified computational framework for defining norms that promote such structures. More specifically, we develop…
We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime…
Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
In this work, we consider learning over multitask graphs, where each agent aims to estimate its own parameter vector. Although agents seek distinct objectives, collaboration among them can be beneficial in scenarios where relationships…
The third medium contact method has recently come into popularity as an alternative to traditional contact methods in contexts where search for contact boundaries is problematic, i.e. topology optimization. To enforce the contact…
In this article we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector valued one-forms. We provide a numerical framework for the computation…
The Material Point Method (MPM) is a hybrid Eulerian Lagrangian simulation technique for solid mechanics with significant deformation. Structured background grids are commonly employed in the standard MPM, but they may give rise to several…
High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension…
We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping ${\bf r}$ from a two dimensional parameter space $M$ to the three dimensional Euclidean space ${\bf R}^3$. The…