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We extend the simplex-in-cell (SIC) technique recently introduced in the context of collisionless dark matter fluids (Abel et al. 2012; Hahn et al. 2012) to the case of collisionless plasmas. The six-dimensional phase space distribution…
A method for designing transformation electromagnetics devices using tensor impedance surfaces (TISs) is presented. The method is first applied to idealized tensor impedance boundary conditions (TIBCs), and later to printed-circuit tensor…
In integrating topological insulators (TIs) with conventional materials, one crucial issue is how the topological surface states (TSS) will behave in such heterostructures. We use first-principles approaches to establish accurate tunability…
A hybrid surface integral equation partial differential equation (SIE-PDE) formulation without the boundary condition requirement is proposed to solve the transverse magnetic (TM) electromagnetic problems. In the proposed formulation, the…
This paper is concerned with the problem of an acoustic wave scattering in a locally perturbed periodic structure. As the total wavefield is non-quasi-periodic, effective truncation techniques are pursued for high-accuracy numerical…
Topological insulators (TIs) are a class of materials characterized by an insulting bulk and high mobility topologically protected surface states, making them promising candidates for future optoelectronic and quantum devices. Although…
We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…
We introduce a new "convolution spline" temporal approximation of time domain boundary integral equations (TDBIEs). It shares some properties of convolution quadrature (CQ), but instead of being based on an underlying ODE solver the…
The superior ability of nanostructures to manipulate light has propelled extensive applications in nano-electromagnetic components and devices. Computational electromagnetics plays a critical role in characterizing and optimizing the…
In this work, we have carried out a two-dimensional (2D) simulation of thermal instability (TI) in interstellar matter (ISM), considering it to be a weakly ionised inviscid plasma with radiation loss. We carry out the simulation using our…
Volume integral equations have been used as a theoretical tool in scattering theory for a long time. A classical application is an existence proof for the scattering problem based on the theory of Fredholm integral equations. This approach…
The electric field integral equation is a well known workhorse for obtaining fields scattered by a perfect electric conducting (PEC) object. As a result, the nuances and challenges of solving this equation have been examined for a while.…
Backward stochastic Volterra integral equations (BSVIEs in short) are studied. We introduce the notion of adapted symmetrical solutions (S-solutions in short), which are different from the M-solutions introduced by Yong [17]. We also give…
We propose an anisotropic interfacial continuum solvation (AICS) model to simulate the distinct in-plane and out-of-plane dielectric constants of liquids near solid-liquid interfaces and their spatial variations along the surface normal…
A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement. During such phases, both…
We introduce the concept of Metasurface Absorbing-Boundary Condition (MS-ABC). This represents the first application of metasurface technology to computational electromagnetics. MS-ABCs have similar performance as previously reported…
Fast surface integral equation (SIE) solvers seem to be ideal approaches for simulating 3-D nanophotonic devices, as these devices generate fields both in an interior channel and in the infinite exterior domain. However, many devices of…
We introduce the concept of nonreciprocal nongyrotropic phase gradient metasurfaces. Such metasurfaces are based on bianisotropic phase shifting unit cells, with the required nonreciprocal and nongyrotropic characteristics. Moreover, we…
The general synthetic iterative scheme (GSIS) has proven its efficacy in modeling rarefied gas dynamics, where the steady-state solutions are obtained after dozens of iterations of the Boltzmann equation, with minimal numerical dissipation…
The simulation of fluid flow problems, specifically incompressible flows governed by the Navier-Stokes equations (NSE), holds fundamental significance in a range of scientific and engineering applications. Traditional numerical methods…