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From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…
In tiny metallic nanostructures, quantum confinement and nonlocal response change the collective plasmonic behavior with important consequences for e.g. field-enhancement and extinction cross sections. We report on our most recent…
Classical electromagnetic boundary conditions (EMBCs) fail to describe quantum interface phenomena at nanoscale. Here, we construct the interface model with a transition layer describing the electromagnetic field inhomogeneity across the…
For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…
A boundary element method based on a Green's function technique is introduced to compute resonances with intermediate lifetimes in quasi-two-dimensional dielectric cavities. It can be applied to single or several optical resonators of…
In this paper, we discuss multiscale methods for nonlinear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are…
We present a robust immersed boundary (IB) method for high density ratio multiphase flows that is capable of modeling complex wave-structure interaction (WSI) problems arising in marine and coastal engineering applications. The IB/WSI…
Empirical Green's functions (EGFs) extracted from seismic ambient noise have been widely used to image Earth's interior structures, and the resolution of EGF-based tomography depends on the spatial density of seismic stations. However, due…
We present a simple modification of the direct-forcing immersed boundary method (IBM) proposed by Uhlmann [J. Comput. Phys, 2005] in order to enable it to be applied to particulate flows with solid-to-fluid density ratios around unity. The…
We apply the generalized method of separation of variables (GMSV) to solve boundary value problems for the Laplace operator in three-dimensional domains with disconnected spherical boundaries (i.e., an arbitrary configuration of…
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…
An accelerated boundary integral method for Stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry. The computational complexity of the…
Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling…
This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…
In this work we consider how surface-adherent bacterial biofilm communities respond in flowing systems. We simulate the fluid-structure interaction and separation process using the immersed boundary method. In these simulations we model and…
It has recently been demonstrated that difference frequency mixing (DFM) can generate surface plasmons in graphene [1]. Here, we present detailed calculations comparing the contributions to this effect from substrate and from graphene…
Understanding light-matter interaction at the nanoscale requires probing the optical properties of matter at the individual nano-absorber level. To this end, we have developed a nanomechanical photothermal sensing platform that can be used…
Geometrical singularities in plasmonic metasurfaces have recently been proposed for the enhancement of light-matter interactions, owing to their broadband light-harvesting properties and extreme plasmon confinement. However, the large…
We present the applications of nonlinear local harmonic analysis methods to the modelling of beam-beam interaction. Our approach is based on methods provided the possibility to work with dynamical beam localization in phase space. The…