The goals of this seminar are to expose students, postdocs, faculty and visitors to research about waves broadly speaking in a interdisciplinary setting. Topics include non linear waves, applications in acoustics, optics, etc. This seminar also provides opportunities to share interesting findings, and to potentially contribute with research ideas/projects.
Our group meetings and seminar are led by Chrysoula Tsogka and Symeon Papadimitropoulos and consist of graduate students, postdocs and faculty.
For the Fall 2022 semester, seminars will take place on Tuesdays from 3pm to 4pm in Conference room 362B (ACS building) or via zoom.
September 27: Elsie Cortes (University of California, Merced)
Title: Boundary Integral Equation Methods for Optical Cloaking Models
Abstract: Optical cloaking refers to the act of making an object invisible by preventing the light scattering in some directions as it hits the object. While our main interest is optical cloaking, this idea can be extended to other contexts such as radar and imaging. Developing a model to accurately capture cloaking comes with numerical challenges, however. In our model, we must determine how light propagates through a medium composed by multiple, thin layers of materials with different electromagnetic properties. In this talk we consider a multi-layered scalar transmission problem in 2D and use boundary integral equation (BIE) methods to compute the total field. The Kress product quadrature rule  is used to approximate singular integrals evaluated on boundaries, while in the layer we employ the Boundary Regularized Integral Equation Formulation (BRIEF) method  with Periodic Trapezoid Rule (PTR) to treat nearly singular ones appearing in the representation formula. Numerical results illustrate the efficiency of this approach, which may be applied to N arbitrary smooth layers.
 Kress, R. Boundary integral equations in time-harmonic acoustic scattering. 1991. Mathematical and Computer Modelling.
 Sun Q., Klaseboer E., Khoo B. C., and Chan D. Y. C. 2015. Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.
September 13: Arnold D. Kim (University of California, Merced)
Title: Tunably high-resolution synthetic aperture imaging
We begin by reviewing a quantitative signal subspace imaging for multifrequency synthetic aperture imaging. The key to this method is a pre-processing step that rearranges the frequency response at each spatial location using the Prony method which produces a matrix that is suitable for quantitative signal subspace methods. This method also involves a user-defined parameter that can be used to tune the resolution. However, this method is limited to problems where the signal can be reliably distinguished from noise. To consider more general problems, we identify the elementary mechanism in this quantitative signal subspace method that leads to tunable resolution which allows us to propose a simple extension to Kirchhoff migration. This modification to Kirchhoff migration produces tunably high-resolution images for larger ranges of signal-to-noise ratios. We show numerical simulations that demonstrate the utility of these methods
For the Spring 2022 semester, seminars will take place on Thursdays from 2pm to 3pm in Conference room 362B (ACS building) or via zoom.
January 27: Marie Graff (University of Auckland)
Title: Two methods to reconstruct wavefields from measurements, using absorbing boundary conditions in an unusual way
Starting from classical absorbing boundary conditions, we propose two methods to reconstruct wavefields from recorded data. The usual purpose of absorbing boundary conditions is to model an infinite domain while computing numerical solutions on a finite mesh grid. In these two methods, we divert the role of these conditions. The first method, called TRAC, allows us to reconstruct the wavefield everywhere in the domain from measurements at the boundary (modulo a well-chosen sink). The second method, called wave splitting, allows us to split the total wavefield measured on some boundary into its incident and scattered components. Both methods have been combined with an inverse problem solver to answer the following question: "How to solve inverse scattering problems without knowing the source term?"
Numerical results in time-dependent two-space dimensions are presented to illustrate each method.
February 10: Arnold D. Kim (UC Merced)
Title: Direct and inverse obstacle scattering
We discuss elementary aspects of scattering by a particle. Using that knowledge of the direct scattering problem, we then consider the inverse scattering problem for synthetic aperture imaging systems. Instead of using measurements to reconstruct the boundary of the obstacle, we study the structure of the frequency spectrum of the measurements and propose a spectroscopic-based approach to distinguish different material and shape characteristics of particles. We present some preliminary simulation results and identify open problems to pursue.
February 24: Russel Luke (University of Göttingen)
Title: Wavefront Sensing on the James Webb Space Telescope
Abstract: We present the theory and practice of fine wavefront sensing for the JWST.
March 10: Daniel Appelö (Michigan State University)
Title: WaveHoltz: Parallel and Scalable Solution of the Helmholtz Equation via Wave Equation Iteration
Abstract: We introduce a novel idea, the WaveHoltz iteration, for solving the Helmholtz equation. Our method makes use of time domain methods for wave equations to design frequency domain Helmholtz solvers. We show that the WaveHoltz iteration we propose results in a symmetric and positive definite linear system even though we are solving the Helmholtz equation. As our method utilizes time-domain solvers we can exploit features such as local timestepping that are not present in the frequency domain. A unique “free lunch” property that WaveHoltz possesses allows us to solve for multiple frequencies at the cost of a single solve. We will present numerical examples, using various discretization techniques, that show that our method can be used to solve problems with rather high wave numbers.
March 31: Zoi-Heleni Michalopoulou (New Jersey Institue of Technology, NJIT)
Title: Inverse problems in ocean acoustics: particle filtering and linearization for parameter estimation
Abstract: Solving the inverse problem in ocean acoustics, that is, obtaining from received acoustic fields parameters that are related to source location and the environment is a complex non-linear problem. Efficiency and accuracy depend on the nature of the available data and the forward model employed in the inversion. Full-field methods (such as Matched Field Processing) have been used in the past to solve such problems but those can be prone to errors due to the parameterization of the propagation medium and are often computationally inefficient. To circumvent the use of full fields, we develop a method that extracts ray path arrival times from received fields; particle filtering is the foundation of the approach. Probability density functions of arrival times computed via particle filtering are propagated backward through the proposed inversion process, which is conducted after linearizing the forward model. We discuss the computation of the Jacobian matrix, which is necessary for the linearization process. With the sequential filter providing full probability density functions of arrival times, we are able to obtain full probability densities of the unknown parameter, which enable uncertainty quantification in the inversion process.
April 14: Daisy Duarte (UC Merced) /Elsie Cortes (UC Merced)
April 28: François Monard (UC Santa Cruz)
Title: Sampling the X-ray transform on simple surfaces
Abstract: On a Riemannian manifold-with-boundary, the geodesic X-ray transform maps a function to the collection of its integrals over all geodesics through the domain. The problem of inverting this transform arises in medical imaging (e.g., X-ray CT, SPECT) and seismology (e.g., linearized travel-time tomography). In the literature, it is now well-known that injectivity, stability (or mild instability) and inversion formulas hold at the continuous level, for example when $(M,g)$ is a 'simple' surface. By 'simple' we mean (i) no infinite-length geodesic, (ii) no conjugate points, (iii) strictly geodesically convex boundary, arguably the most inversion-friendly case. The question of interest becomes to address numerical inversion from discrete data, where sampling issues arise.
In this talk, I will discuss the issue of proper discretizing and sampling related to geodesic X-ray transforms on simple surfaces, addressing the following questions:
(a) Given a bandlimited function $f$, what are the minimal sampling rates needed on its X-ray transform $I_0 f$ for a faithful (=unaliased) recovery?
(b) In the case where data is sampled below the expected requirements, can one predict the location, orientation and frequency of the artifacts generated?
The main tools to answer (a)-(b) are a combination of a reinterpretation of the classical Shannon-Nyquist theorem in semi-classical terms, as initiated by Plamen Stefanov in , and an accurate description of the canonical relation of the X-ray transform viewed as a (classical, then semi-classical) Fourier Integral Operator. Focusing on constant curvature surfaces as a first family of examples, we quantify the quality of a sampling scheme depending on geometric parameters of the surface (e.g., curvature and boundary curvature), and on the coordinate system used to represent the space of geodesics. Several (unaliased and aliased) examples will be given throughout.
Joint with Plamen Stefanov (Purdue). Preprint available at https://arxiv.org/pdf/2110.05761.pdf
 P. Stefanov, Semiclassical sampling and discretization of certain linear inverse problems. SIAM J. Math. Anal., 52(6), 5554-5597, 2020.
For the Fall 2021 semester, seminars will take place on Thursdays from 2pm to 3pm in Conference room 362B (ACS building).
September 16: Arnold D. Kim (UC Merced)
Title: Quantitative signal subspace imaging
September 30: Boaz Ilan (UC Merced)
October 14: Pierre-David Letourneau (Reservoir Labs)
Title: Fast Multipole Method (FMM) for simulation of electromagnetic waves in 3D complex media
Abstract: In this talk, I will provide an overview of the Fast Multipole Method (FMM) algorithm and will discuss its use for the simulation of electromagnetic waves in 3D complex media. I will also discuss some recent results obtained in collaboration with UC Merced and Stanford demonstrating how such algorithms can be used for simulating the macroscopic response of materials directly from microstructure. FMMs represent a family of powerful algorithms that allow for the solution of N-body problems in optimal linear time (O(N)). The FMM was originally designed to address the Laplace potential (e.g. gravitational, 1/r) and has since been generalized in various ways. In this presentation, I will focus on the use of the FMM for simulating electromagnetic waves in 3D media consisting of a large number of disparate discrete scatterers. The talk will begin with an overview of tree-based FMM codes, followed by a description of its specialization to scalar waves and, finally, vector waves (Maxwell's equations). I will also introduce the concept of T-matrix and Foldy-Lax system for the efficient treatment of multiple scattering. Numerical results will demonstrate the advantageous empirical scaling of our implementation in practice, and examples will be provided that demonstrate how it is now possible to capture the macroscopic and asymptotic behaviors of electromagnetic waves from first principles, including in the effective medium and diffusion regimes.
October 28: Cory McCullough, Elsie Cortes (UC Merced)
Title: Scattering by Two Closely Situated Sound-Hard Spheres
Title: Extended BIE System for Scattering in Multilayered Media
November 18: Benjamin Latham (UC Merced)
Title: Subtraction method for computing spherical surface plasmons excitation
For the Spring 2021 semester, seminars will take place on Thursdays from 15:00 to 16:00am via Zoom.
February 4: Adar Kahana (Tel Aviv University)
Title: Solving PDE related problems using deep-learning
Abstract: In this talk I will present our work on PDE related problems and how integrating deep-learning can help achieve better results. We discuss the accelerating topic of physically-informed neural networks: a method for solving PDEs with neural networks. With this in mind, we present our work in this field and present two interesting variants of this method. Motivated by the physical experiment of acoustic waves propagating in an underwater homogeneous domain, we discuss the inverse problem: Simulating the physical experiment, we solve the acoustic wave equation and save the data at a small number of sensors over many time steps and given these sensor measurements we aim to find and identify the shape of an obstacle inside the domain. We cast it to a data-driven problem by building an image segmentation of the domain where the segment is an arbitrary polygon (the obstacle). We improve the model using a physically-informed loss term designed based on the wave equation. After that we switch to a completely different area - we discuss an explicit nonlinear numerical scheme for the 1D wave equation that remains stable when violating the CFL condition. We create a data-set based on a stable wave propagation process and train a network to infer a non-stable process. We incorporate a physically-informed loss term here as well to achieve better accuracy (lower deviation from the analytic solution) for our scheme.
February 18: Remi Cornaggia (Sorbonne University)
Title: Modeling and controlling dispersive waves in architected materials : second-order homogenization and topological optimization
We are interested in waves in two-phase periodic materials, whose phase distribution is to be optimized to obtain specific dispersive properties (typically, to maximize the dispersion in given directions of wave propagation).
The two-scale asymptotic homogenization procedure will first be recalled. In particular, the second-order asymptotic expansion enables to model the low-frequency dispersive behavior of waves in these media. Illustratrations will be given for bilaminates in 1D, for which we designed correctors for boundary and transmission conditions, that complement the wave model to obtain an overall second-order approximation in bounded domains .
The topological optimization algorithm  will then be presented for scalar waves in 2D media (e.g. acoustic or antiplane shear waves). First, simple dispersion indicators are extracted from the homogenized model. Cost functionals to be minimized to achieve certain goals are then defined using these indicators. The minimization is then performed thanks to an iterative algorithm, which relies on the concept of topological derivative (TD) of the cost functional. The TD quantifies the sensitivity of the functional to a localized phase change in the unit cell, and therefore indicates optimal locations where to perform these phase changes. The TD of the cost functionnal can be computed from the TDs of the coefficients of the homogenized model, whose expressions were determined in a previous work . At each step, the cell problems underlying the homogenized model, whose solutions are needed to compute the TDs, are solved thanks to FFT-accelerated solvers .
Two applications of the method will be presented: maximizing the dispersion in given directions, and determining the microstructure of an architected material from phase velocity measurements.
 Second-order homogenization of boundary and transmission conditions for one-dimensional waves in periodic media,
Remi Cornaggia and Bojan B. Guzina, International Journal of Solids and Structures, 2020
 Tuning effective dynamical properties of periodic media by FFT-accelerated topological optimization,
Rémi Cornaggia, Cédric Bellis, International Journal for Numerical Methods in Engineering, 2020
 Microstructural topological sensitivities of the second-order macroscopic model for waves in periodic media.
Marc Bonnet, Rémi Cornaggia and Bojan B. Guzina, SIAM Journal on Applied Mathematics, 2018
 A numerical method for computing the overall response of nonlinear composites with complex microstructure,
Hervé Moulinec et Pierre Suquet, Computer Methods in Applied Mechanics and Engineering, 1998
(files of [1,2,3] available on HAL : https://cv.archives-ouvertes.fr/remi-cornaggia )
March 4: No seminar due to the Conference SIAM CSE
March 18: Pedro Gonzalez Rodriguez (Universidad Carlos III de Madrid)
Title: Solving the Helmholtz equation using RBF-FD
Abstract: In this talk I am going to explain the RBF-FD method starting from the basic RBF interpolation and finishing with the use of polyharmonic splines combined with polynomials. Finally I will apply it to solve the Helmholtz equation and show some results.
April 8 :
Benjamin Latham (UC Merced)
Title: Finite element methods for 3D plasmonic problems
Cory McCullough (UC Merced)
Title: Near-Field Acoustic Scattering by Sound Hard Spheres
April 22: Elsie Cortes (UC Merced)
Title: Modeling Scattering Problems for Multilayered Media
May 6: Imaging and Sensing journal club
For the Fall 2020 semester, seminars will take place on Thursdays from 10:30am to 11:30am via Zoom.
September 3: Sean Horan (UCM)
Title: Double Spherical Harmonics And The Radiative Transport Equation
September 17: Arnold Kim (UCM)
Title: Direct and inverse scattering of extended objects
Both the direct and inverse scattering problems for extended objects are challenging problems. In this talk, I discuss the method of fundamental solutions for the direct scattering problem and signal subspace methods for the inverse scattering problem. The key to both of these methods is knowing the fundamental solution of the governing PDE. I will show some recent results for propagating waves and diffuse waves and discuss some ongoing research going on in the Sensing and Imaging SMaRT team.
Title: Green’s function for nonimaging optics
Abstract: Nonimaging optics has application to designing solar energy concentrators and illumination engineering. In this talk, I will discuss how nonimaging optics can be described in the context of radiative transfer theory. The radiative transport equation reduces to a local transport equation, whose solution can be expressed in terms of a Green’s function. This new formalism may be useful for nonimaging designs.
October 15: Stéphanie Chaillat-Loseille (UMA, ENSTA ParisTech)
Title: Recent advances on the preconditioning of 3D fast Boundary Element Solvers for 3D acoustics and elastodynamics
Abstract: Recent works in the Boundary Element Method (BEM) community have been devoted to the derivation of fast techniques to perform the matrix vector product needed in the iterative solver. Fast BEMs are now very mature. However, it has been shown that the number of iterations can significantly hinder the overall efficiency of fast BEMs. The derivation of robust preconditioners is now inevitable to increase the size of the problems that can be considered. I will present some recent works on analytic and algebraic preconditioners for fast BEMs.
October 29: Ornella Mattei
Title: Wave propagation in space-time microstructures: the theory of field patterns
Abstract: Field patterns are a new type of wave propagating in one-dimensional linear media with moduli that vary both in space and time. Specifically, the geometry of these space-time materials is commensurate with the slope of the characteristic lines so that a disturbance does not generate a complicate cascade of subsequent disturbances, but rather concentrates on a periodic space-time pattern, that we call field pattern. Field patterns present spectacularly novel features. One of the most interesting ones is the appearance of a wave generated from an instantaneous source, whose amplitude, unlike a conventional wake, does not tend to zero away from the wave front. Furthermore, very interestingly, the band structure associated with these special space-time geometries is infinitely degenerate: associated with each point on the dispersion diagram is an infinite space of Bloch functions, a basis for which are generalized functions each concentrated on a field pattern.
November 12: Tomas Virgen (UCM)
Title: Time-Dependent Scattering By A Sound-Hard Sphere
Abstract: Time-dependent scattering in three dimensions is a difficult mathematical problem to solve analytically and numerically. Analytical solutions obtained using the method of separation of variables are complicated, and numerical methods to solve this problem have challenges for computing solutions at long distances and long times. We seek a simple, effective, and efficient method to solve this problem based on the method of fundamental solutions. The specific case of a sound-hard sphere is considered in the context of acoustics.
December 3: Camille Carvalho
Title: Limiting Amplitude Principle for plasmonic structures with corners
Seminars are on Thursdays, 2pm-3pm in ACS 362B.
February 6: Dr. Nicki Boardman, 2pm-3pm in Granite Pass 120-125
February 20: Matthias Bussonnier
Title: Python overview
Title: Subtraction tecnhiques for the close evaluation of layer potentials
Abstract: Close evaluation of layer potentials reffer to large errors occured at evaluation points near (but not on) the boundary. This is due to peaked behaviors of the integrands near the boundary. There exist subtraction techniques to smooth out the peaked behavior for Laplace's problems. In this talk we present how to extend those ideas to waves problems.
Arnold D. Kim
Title: Optical imaging of colloids
Abstract: A colloidal suspension is a collection of nanometer to micron scaled particles in a fluid used to study self-assembly. A key to studying colloids lies in imaging these particles accurately and efficiently within a standard microscope setup. In this talk, we introduce this imaging problem, propose an imaging method that uses space, angle or wavelength diversity at the source to compensate for the intensity-only measurements, and demonstrate its effectiveness through numerical simulations.
March 19: Cancelled
April 9: Lori Lewis
Title: Asymptotic approximations for boundary integral equations with regions of high curvature
Title: Introduction to Surface Plasmons on a Planar Interface
Title: Where are the plasmons: asymptotics for the cavity case
The first meeting will be on Thursday, September the 12th, at 10-11am in ACS 362B. The first meeting will be an organizational
meeting and introductions. The focus of this meeting will be on setting up the schedule, hence we'll need volunteers to give talks. If you can't make this meeting but would like to give a talk, please send me your title and preferred date as soon as possible.
Arnold D. Kim, (Full Professor, Applied Mathematics, University of California, Merced)
Title Talk: Research projects about the multiple scattering of light
Abstract: In this talk I give an overview of my research projects about the multiple scattering of light. Then I discuss two specific projects in detail. First, I discuss modeling nano cloaking structures in collaboration with Prof. Ghosh's lab. Then I discuss some recent work in the diffuse optical imaging of tissues using spatially modulated light.
Chrysoula Tsogka, (Full Professor, Applied Mathematics, University of California, Merced)
Title Talk: Imaging in waveguides
Boaz Ilan, (Full Professor, Applied Mathematics, University of California, Merced)
Title Talk: Nonlinear eigenvalue problems in nonlinear waves
Jay Sharping, (Professor, Physics, University of California, Merced)
Title Talk: Tunable SRF cavities for 3D optomechanics
Abstract: Quantum mechanics is real! If you took a physics class on Quantum Mechanics, they (should have) told you to consider a mass on a spring and (should have) showed that the energy spectrum for that thing is quantized. Over the past 10 years or so we have finally been able to do just that in the lab. One of my research goals is to combine low loss oscillators such as optical or microwave cavities with mechanical oscillators in hopes of one day recognizing quantum behavior in large oscillators. In this talk I will (hopefully) get you excited about the prospects of this effort and then share designs, simulations and experiments with high-Q 3-dimensional cavities. I’ll give you a status report on my group’s journey to coupling these cavities to mechanical oscillators.
Zoïs Moitier, (Postdoc, Applied Mathematics, University of California, Merced)
Title : Asymptotic expansions of Whispering Gallery Modes optical micro-cavities
Abstract: In this talk we study the resonance frequencies of bidimensional optical cavities. More specifically, we are interested in whispering-gallery modes (modes localized along the cavity boundary with a large number of oscillations). The first part deals with the numerical computation of resonances by the finite element method using perfectly matched layers, and with a sensibility analysis in the three following situations: an unidimensional problem, a reduction of the rotationally invariant bidimensional case, and the general case. The second part focuses on the construction of asymptotic expansions of whispering-gallery modes as the number of oscillations along of boundary goes to infinity. We start by considering the case of a rotationally invariant problem for which the number of oscillations can be interpreted as a semiclassical parameter by means of an angular Fourier transform. Next, for the general case, the construction uses a phase-amplitude ansatz of WKB type which leads to a generalized Schrödinger operator. Finally, the numerically computed resonances obtained in the first part are compared to the asymptotic expansions made explicit by the use of a computer algebra software.
Cory MacCullough, (graduate student, Applied Mathematics, University of California, Merced)
Title Talk: TBA
Imran Khan, (graduate student, Physics, University of California, Merced)
Title Talk: TBA
Title Talk: TBA