Jaume Peraire - Academia.edu (original) (raw)

Papers by Jaume Peraire

The design of metamaterials is currently a fertile research domain. However, most of the metamate... more The design of metamaterials is currently a fertile research domain. However, most of the metamaterial designs described in the literature arise from physical intuition, and often assume infinite periodicity. There is therefore a need for a design methodology capable of computing patterns and designs involving two different materials where the underlying design variables correspond to a finite set of pixels in a 2-dimensional mesh, and where the goal is a design with prescribed metamaterial properties. This naturally leads to the consideration of binary optimization models in contrast to classical (continuous) gradient-based methods which generically provide continuous solutions that then need to be “rounded” to binary values. While the potential drawback of binary optimization is that its computational complexity is usually NP-hard and hence theoretically unattractive, we show herein that binary optimization combined with a reduced basis approach can relatively efficiently produce v...

AIAA Scitech 2020 Forum, 2020

We present a wall-resolved implicit large eddy simulation (WRILES) of transonic buffet over the O... more We present a wall-resolved implicit large eddy simulation (WRILES) of transonic buffet over the OAT15A supercritical airfoil at at Mach number 0.73, angle of attack 3.5rmo3.5^{\rm o}3.5rmo and Reynolds number 3times1063 \times 10^63times106. The simulation is performed using a high-order discontinuous Galerkin (DG) method and a diagonally implicit Runge-Kutta (DIRK) scheme on graphics processor units (GPUs). In order to effectively resolve the boundary layers at high Reynolds numbers, we develop a LES mesh refinement strategy to provide adequate resolution in the normal and streamwise/crossflow directions while keeping the aspect ratio of the elements below 20. Without yhe need for subgrid scale or wall models, the WRILES method successfully predicts the buffet onset, the buffet frequency, and turbulence statistics. Various turbulence phenomena are predicted and demonstrated, such as periodical low-frequency oscillations of shock wave in the streamwise direction, strong shear layer detached from the shock wave due to shock wave boundary layer interaction (SWBLI) and small scale structures broken down by the shear layer instability in the transition region, and shock-induced flow separation. The pressure coefficient, the root mean square (RMS) of fluctuating pressure and streamwise range of shock wave oscillation agree well with experimental data. The results demonstrate the capability of the WRILES method for predicting the buffet phenomena at high Reynolds numbers.

Proceedings of the 22nd International Meshing Roundtable, 2014

A procedure to quantify the distortion (quality) of a high-order mesh composed by curved tetrahed... more A procedure to quantify the distortion (quality) of a high-order mesh composed by curved tetrahedral elements is presented. The proposed technique has two main applications. First, it can be used to check the validity and quality of a high-order tetrahedral mesh. Second, it allows the generation of curved meshes composed by valid and high-quality high-order tetrahedral elements. To this end, we describe a method to simultaneously smooth and untangle high-order tetrahedral meshes by minimizing the proposed mesh distortion. Finally, we present several results to illustrate the two main applications of the proposed technique.

Physical Review E, 2011

We present and use an algorithm based on convex conic optimization to design two-dimensional phot... more We present and use an algorithm based on convex conic optimization to design two-dimensional photonic crystals with large absolute band gaps. Among several illustrations we show that it is possible to design photonic crystals which exhibit multiple absolute band gaps for the combined transverse electric and magnetic modes. The optimized crystals show complicated patterns which are far different from existing photonic crystal designs. We employ subspace approximation and mesh adaptivity to enhance computational efficiency. For some examples involving two band gaps, we demonstrate the trade-off frontier between two different absolute band gaps.

Journal of Computational Physics, 2010

In this paper, we consider the optimal design of photonic crystal band structures for twodimensio... more In this paper, we consider the optimal design of photonic crystal band structures for twodimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized using the finite element method into a series of finite-dimensional eigenvalue problems for multiple values of the wave vector parameter. The resulting optimization problem is large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigenspaces, we reduce the large-scale non-convex optimization problem via reparametrization to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP solvers can be efficiently applied. Numerical results are presented for both transverse magnetic (TM) and transverse electric (TE) polarizations at several frequency bands. The optimized structures exhibit patterns which go far beyond typical physical intuition on periodic media design.

International Journal for Numerical Methods in Fluids, 1987

A high resobtt ion finite element method for t he solut ion of problems involving high _pe_! comp... more A high resobtt ion finite element method for t he solut ion of problems involving high _pe_! compressible flows is pre_nted. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm.

International Journal for Numerical Methods in Fluids, 1999

This paper investigates robust consensus for multi-agent systems with discrete-time dynamics affe... more This paper investigates robust consensus for multi-agent systems with discrete-time dynamics affected by uncertainty. In particular, the paper considers multi-agent systems with single and double integrators, where the weighted adjacency matrix is a polynomial function of uncertain parameters constrained into a semialgebraic set. Firstly, necessary and sufficient conditions are provided for robust consensus based on the existence of a Lyapunov function polynomially dependent on the uncertainty. In particular, an upper bound on the degree required for achieving necessity is provided. Secondly, a necessary and sufficient condition is provided for robust consensus with single integrator and nonnegative weighted adjacency matrices based on the zeros of a polynomial. Lastly, it is shown how these conditions can be investigated through convex programming by exploiting linear matrix inequalities and sums of squares of polynomials. Some numerical examples illustrate the proposed results.

AIAA Scitech Forum, 2020

In this paper, we present a Hybridizable Discontinuous Galerkin (HDG) method for the solution of ... more In this paper, we present a Hybridizable Discontinuous Galerkin (HDG) method for the solution of the compressible Euler and Navier-Stokes equations. The method is devised by using the discontinuous Galerkin approximation with a special choice of the numerical fluxes and weakly imposing the continuity of the normal component of the numerical fluxes across the element interfaces. This allows the approximate conserved variables defining the discontinuous Galerkin solution to be locally condensed, thereby resulting in a reduced system which involves only the degrees of freedom of the approximate traces of the solution. The HDG method inherits the geometric flexibility and arbitrary high order accuracy of Discontinuous Galerkin methods, but offers a significant reduction in the computational cost as well as improved accuracy and convergence properties. In particular, we show that HDG produces optimal converges rates for both the conserved quantities as well as the viscous stresses and the heat fluxes. We present some numerical results to demonstrate the accuracy and convergence properties of the method.

International Journal of Computational Fluid Dynamics

Communications in Applied Numerical Methods

An artificial viscosity suitable for use in the simulation of multidimensional high-speed compres... more An artificial viscosity suitable for use in the simulation of multidimensional high-speed compressible flows by the finite element method is proposed. The form adopted is a consistent extension of the method due to Lapidus.

REPORT DOCUMENTATION PAGE_ 3ublic reporting burden for this collection of information is estimate... more REPORT DOCUMENTATION PAGE_ 3ublic reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing insti (Q")-. d aintaining the lata needed, and completing and reviewing this collection of information Send comments regarding this burden estimate.or any other as .. uding suggestions for reducing hi s burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-018 ... rghway, Suite 1204, Arlington, VA 22202-1302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing t. ... ,. a collection of information if it does not display a currentli ,alid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON

An interpolation method is presented for the reconstruction and recognition of human face images.... more An interpolation method is presented for the reconstruction and recognition of human face images. Basic ingredients include an optimal basis set defining a low-dimensional face space and a set of "best interpolation pixels" capturing the most relevant characteristics of known faces. The best interpolation pixels are chosen as points of the pixel grid so as to best interpolate the set of known face images. These pixels are then used in a least-squares interpolation procedure to determine interpolant components of a face image very inexpensively, thereby providing efficient reconstruction of faces. In addition, the method allows a fully automatic computer system to be developed for the real-time recognition of faces. Two significant advantages of this method are: (1) the computational cost of recognizing a new face is independent of the size of the pixel grid; and (2) it allows for the reconstruction and recognition of incomplete images.

Journal of Computational Physics

We present a model and variance reduction method for the fast and reliable computation of statist... more We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.

40th Structures, Structural Dynamics, and Materials Conference and Exhibit

A summary of results from five university teams, working over five years is presented. Broadly sp... more A summary of results from five university teams, working over five years is presented. Broadly speaking, we have conducted animal flight tests, neurophysiology of bat flight, model experiments motivated by animal flights (membrane wings, flapping wings, etc), computational simulations of flapping flight at multiple levels of fidelity, and experiments and theory of flapping flight control systems. bats, flapping flight, unsteady aerodynamics, neurophysiology, control theory.