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A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
(2022-11-01)
This work extends an automatic energy-norm $hp$-adaptive strategy based on performing quasi-optimal unrefinements to the case of non-elliptic problems and goal-oriented adaptivity. The proposed approach employs a multi-level ...
1D Painless Multi-level Automatic Goal-Oriented h and p Adaptive Strategies Using a Pseudo-Dual Operator
(2022-01-01)
The main idea of our Goal-Oriented Adaptive (GOA) strategy is based on performing global and uniform h- or p-refinements (for h- and p-adaptivity, respectively) followed by a coarsening step, where some basis functions are ...
An implicit symplectic solver for high-precision long term integrations of the Solar System
(2022)
We present FCIRK16, a 16th-order implicit symplectic integrator for long-term high precision Solar System simulations. Our integrator takes advantage of the near-Keplerian motion of the planets around the Sun by ...
An Algorithm based on continuation techniques for minimization problems with highly non linear equality constraints
(2021)
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to ...
Design of Loss Functions for Solving Inverse Problems using Deep Learning
(2020-05)
Solving inverse problems is a crucial task in several applications that strongly a ffect our daily lives, including multiple engineering fields, military operations, and/or energy production. There exist different methods ...
Variational Formulations for Explicit Runge-Kutta Methods
(2019-08)
Variational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known ...
Explicit-in-Time Goal-Oriented Adaptivity
(2019-04-15)
Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of ...
Forward-in-Time Goal-Oriented Adaptivity
(2019-03)
In goal-oriented adaptive algorithms for partial differential equations, we adapt the finite element mesh in order to reduce the error of the solution in some quantity of interest. In time-dependent problems, this adaptive ...
Time-Domain Goal-Oriented Adaptivity Using Pseudo-Dual Error Representations
(2017-12)
Goal-oriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudo-dual problems for goal-oriented adaptivity in the ...