2 Discretization 9 2.1 The Discontinuous Galerkin Method . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.2 Solution Approximation . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Weak Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.4 Discrete System . . . . . . . . . . . . . . . . . ....

This paper tests a methodology for tsunami waveform inversion, based on the adjoint method. The method is designed to perform the direct optimization of the tsunami fault parameters, from tide-gauge data, imposing strong geophysical constrains to the inverted solutions, leading to a substantial enhancement of the signal-to-noise ratio, when compared with the classical technique based on Green’s...

Adaptivity in space and time is ubiquitous in modern numerical simulations. The large number of unknowns associated with today’s typical inverse problem may run in the millions, or more. To capture small scale phenomena in regions of interest, adaptive mesh and temporal step refinements are required, since uniform refinements quickly make the problem computationally intractable. To date, there ...

The effect of topology on the thermodynamics of a gas of adjoint representation charges interacting via 1+1 dimensional SU (N) gauge fields is investigated. We demonstrate explicitly the existence of multiple vacua parameterized by the discrete superse-lection variable k = 1, · · · , N. In the low pressure limit, the k dependence of the adjoint gas equation of state is calculated and shown to b...

We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, twoand gauge invariant D-dimensional matrix models at large-N and compare them with their bosonic counterparts which are the more familiar Hermitian matrix models. We derive and solve the complete sets of loop equations for the correlators ...