66 research outputs found
Asymptotic Modelling for 3D Eddy Current Problems with a Conductive Thin Layer
Book of abstracts of the 7th International Conference on Advanced Computational Methods in EngineeringInternational audienceIn this work we derive and analyze an equivalent model for 3D Eddy Current problems with a conductive thin layer of small thickness . In our model, the conductive sheet is replaced by its mid-surface and their shielding behavior is satisfied by an equivalent transmission conditions on this interface. The transmission conditions are derived asymptotically for vanishing sheet thickness
A novel Calderón preconditioner for the simulation of conductive and high-dielectric contrast media
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Analysis of L1-difference methods for time-fractional nonlinear parabolic problems with delay
This work is concerned with numerical solutions of time-fractional nonlinear parabolic
problems by a class of L1-difference methods. The analysis of L1 methods for timefractional
nonlinear problems with delay is limited mainly due to the lack of a fundamental
Gronwall type inequality. We establish such a fundamental inequality for the
L1 approximation to the Caputo fractional derivative. In terms of the Gronwall type inequality,
we will provide error estimates of a fully discrete linearized difference scheme
for this kind of problems
Efficient computational homogenisation of 2D beams of heterogeneous elasticity using the patch scheme
Modern 'smart' materials have complex heterogeneous microscale structure,
often with unknown macroscale closure but one we need to realise for large
scale engineering and science. The multiscale Equation-Free Patch Scheme
empowers us to non-intrusively, efficiently, and accurately predict the large
scale, system level, solutions through computations on only small sparse
patches of the given detailed microscale system. Here the microscale system is
that of a 2D beam of heterogeneous elasticity, with either fixed fixed,
fixed-free, or periodic boundary conditions. We demonstrate that the described
multiscale Patch Scheme simply, efficiently, and stably predicts the beam's
macroscale, with a controllable accuracy, at finite scale separation. Dynamical
systems theory supports the scheme. This article points the way for others to
use this systematic non-intrusive approach, via a developing toolbox of
functions, to model and compute accurately macroscale system-levels of general
complex physical and engineering systems
Robust preconditioners for a new stabilized discretization of the poroelastic equations
In this paper, we present block preconditioners for a stabilized
discretization of the poroelastic equations developed in [45]. The
discretization is proved to be well-posed with respect to the physical and
discretization parameters, and thus provides a framework to develop
preconditioners that are robust with respect to such parameters as well. We
construct both norm-equivalent (diagonal) and field-of-value-equivalent
(triangular) preconditioners for both the stabilized discretization and a
perturbation of the stabilized discretization that leads to a smaller overall
problem after static condensation. Numerical tests for both two- and
three-dimensional problems confirm the robustness of the block preconditioners
with respect to the physical and discretization parameters
Phase-field modeling and effective simulation of non-isothermal reactive transport
We consider single-phase flow with solute transport where ions in the fluid
can precipitate and form a mineral, and where the mineral can dissolve and
release solute into the fluid. Such a setting includes an evolving interface
between fluid and mineral. We approximate the evolving interface with a diffuse
interface, which is modeled with an Allen-Cahn equation. We also include
effects from temperature such that the reaction rate can depend on temperature,
and allow heat conduction through fluid and mineral. As Allen-Cahn is generally
not conservative due to curvature-driven motion, we include a reformulation
that is conservative. This reformulation includes a non-local term which makes
the use of standard Newton iterations for solving the resulting non-linear
system of equations very slow. We instead apply L-scheme iterations, which can
be proven to converge for any starting guess, although giving only linear
convergence. The three coupled equations for diffuse interface, solute
transport and heat transport are solved via an iterative coupling scheme. This
allows the three equations to be solved more efficiently compared to a
monolithic scheme, and only few iterations are needed for high accuracy.
Through numerical experiments we highlight the usefulness and efficiency of the
suggested numerical scheme and the applicability of the resulting model
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