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Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
The text offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential…
High-Order Collocation Methods for Differential Equations with Random Inputs
A high-order stochastic collocation approach is proposed, which takes advantage of an assumption of smoothness of the solution in random space to achieve fast convergence and requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods.
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations
The text is focused on formulation, analysis, and computational procedures for reduced basis approximation and a posteriori error estimation for parametrized PDEs in the real-time and many-query…
SPECTRAL METHODS FOR TIME-DEPENDENT PROBLEMS.
This poster presents a meta-anatomy of the EMMARM, a probabilistic model of the immune response to EMT that combines modeled EMT and EMT with real-time information about the immune system.
Certified Reduced Basis Methods for Parametrized Partial Differential Equations
This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from…
Nodal discontinuous Galerkin methods on graphics processors
Nodal high-order methods on unstructured grids
A convergent high-order accurate scheme for the solution of linear conservation laws in geometrically complex domains and demonstrates the versatility, flexibility, and robustness when solving two- and three-dimensional benchmark problems in computational electromagnetics.
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
We present a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere. To overcome well-known problems with polar singularities, we consider the shallow…