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This report focuses on the implementation of the finite element method for nonlinear dynamical problems arising in solid mechanics. The theory of continuum mechanics is extensively covered in the literature and it is assumed the reader is already familiar ...
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of g ...
Soft adhesive pads attached to a rigid substrate show stick-slip behavior upon loading: they detach and reattach in a different location. This is accompanied by the lifting of the adhesive, the mechanical wave carrying this motion being known as a Schallam ...
A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations is introduced. Departing from classical adaptive algorithms, the proposed method is based on a coarse grid and iteratively improves the accuracy of the solution by s ...
The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...
Finite volume methods are proposed for computing approximate pathwise entropy/kinetic solutions to conservation laws with flux functions driven by low-regularity paths. For a convex flux, it is demonstrated that driving path oscillations may lead to "cance ...
We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sparse block matrices and the alternating direction method of multipliers (ADM ...
We investigate the behavior of two coupled nonlinear photonic cavities, in the presence of inhomogeneous coherent driving and local dissipations. By solving numerically the quantum master equation, either by diagonalizing the Liouvillian superoperator or b ...
We present a numerical method for the solution of nonlinear geomechanical problems involving localized deformation along shear bands and fractures. We leverage the boundary element method to solve for the quasi-static elastic deformation of the medium whil ...
High-order numerical solvers for conservation laws suffer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amoun ...
