Related papers: Accuracy and Conditioning of Surface-Source Based …
We present an inverse method to compute freeform optical surfaces that transform a light distribution, parameterized by two source planes, into two separate target distributions. The surfaces can be reflectors or lenses, and control both…
This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer…
The surface errors of freeform surfaces reflect the manufacturing complexities and significantly impact the feasibility of processing designed optical systems. With multiple degrees of freedom, freeform surfaces pose challenges in surface…
We classify the surfaces translating under the flows by sub-affine-critical powers of the Gauss curvature. This, in particular, lists all translating solitons possibly model Type II singularities for convex closed solutions in all positive…
In this paper, we propose an alternative approach to implement the contact angle boundary condition on immersed surfaces for phase-field simulations of two-phase flows using the Cahn-Hilliard equation on a Cartesian mesh. This simple and…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
A uniform derivation is presented of the self-consistent field equations in a finite basis set. Both restricted and unrestricted Hartree-Fock (HF) theory as well as various density functional (DF) approximations are considered. The unitary…
The near-surface environment is often too complex to enable inference of hydrological and environmental variables using one geophysical data type alone. Joint inversion and coupled inverse modeling involving numerical flow- and transport…
Shape from shading is a classical inverse problem in computer vision. This shape reconstruction problem is inherently ill-defined; it depends on the assumed light source direction. We introduce a novel mathematical formulation for…
We report in this paper a fast and accurate algorithm for computing the exact spherical nonreflecting boundary condition (NRBC) for time-dependent Maxwell's equations. It is essentially based on a new formulation of the NRBC, which allows…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
We present a semi-analytical formulation of the interaction between a given source field and a scalar Huygens metasurface (HMS), a recently introduced promising concept for wavefront manipulation based on a sheet of orthogonal electric and…
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…
A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are…
We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap…
We develop a new boundary condition for the weak inverse mean curvature flow, which gives canonical and non-trivial solutions in bounded domains. Roughly speaking, the boundary of the domain serves as an outer obstacle, and the evolving…
We study the inverse problem of qualitatively recovering a supported cavity in a thin elastic plate governed by the flexural (biharmonic) wave equation, using far-field pattern measurements. We derive a reciprocity principle and a…