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The interface control domain decomposition (ICDD) method of Discacciati, Gervasio, and Quarteroni [SIAM J. Control Optim., 51 (2013), pp. 3434-3458, doi:10.1137/120890764; J. Coupled Syst. Multiscale Dyn., 1 (2013), pp. 372-392, doi:10.1166/jcsmd.2013.1026 ...
We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used ...
Causal consistency is one of the most adopted consistency criteria for distributed implementations of data structures. It ensures that operations are executed at all sites according to their causal precedence. We address the issue of verifying automaticall ...
Formal verification utilizing symbolic computer algebra has demonstrated the ability to formally verify large Galois field arithmetic circuits and basic architectures of integer arithmetic circuits. The technique models the circuit as Gröbner basis polynom ...
Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curv ...
We review spectral methods for the solution of hyperbolic problems. To keep the discussion concise, we focus on Fourier spectral methods and address key issues of accuracy, stability, and convergence of the numerical approximations. Polynomial methods are ...
Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...
We consider a finite element method (FEM) with arbitrary polynomial degree for nonlinear monotone elliptic problems. Using a linear elliptic projection, we first give a new short proof of the optimal convergence rate of the FEM in the L2 norm. We then deri ...
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of th ...
Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of ``interpretable" signals along with ...
Institute of Electrical and Electronics Engineers2016