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Exploiting the Kronecker product structure of φ−functions in exponential integrators
(2022-05-15)
Exponential time integrators are well-established discretization methods for time semilinear systems of ordinary differential equations. These methods use (Formula presented.) functions, which are matrix functions related ...
A space-time DPG method for the wave equation in multiple dimensions
(2019)
A space-time discontinuous Petrov–Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The well-posedness of this formulation is ...
Asymptotic Models for the Electric Potential across a Highly Conductive Casing
(2018-07)
We analyze a configuration that involves a steel-cased borehole, where the casing that covers the borehole is considered as a highly conductive thin layer. We develop an asymptotic method for deriving reduced problems ...
A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
(2018-06-14)
In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a ...
Discrete maximum principles for nonlinear parabolic PDE systems
(2012-12-31)
Discrete maximum principles (DMPs) are established for finite element approximations of systems of nonlinear parabolic partial differential equations with mixed boundary and interface conditions. The results are based on ...