A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems

We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal-oriented a posteriori error indicators are presented. The examples presented clearly demonstrate the capabilities and the benefits of combining our pre-processing mesh movement algorithm with both uniform, as well as, adaptive isotropic and anisotropic mesh refinement.

Artificial Immune Tissue using Self-Organizing Networks

As introduced by Bentley et al. (2005), artificial immune systems (AIS) are lacking tissue, which is present in one form or another in all living multi-cellular organisms. Some have argued that this concept in the context of AIS brings little novelty to the already saturated field of the immune inspired computational research. This article aims to show that such a component of an AIS has the potential to bring an advantage to a data processing algorithm in terms of data pre-processing, clustering and extraction of features desired by the immune inspired system. The proposed tissue algorithm is based on self-organizing networks, such as self-organizing maps (SOM) developed by Kohonen (1996) and an analogy of the so called Toll-Like Receptors (TLR) affecting the activation function of the clusters developed by the SOM.

Artificial Immune Tissue using Self-Organizing Networks

As introduced by Bentley et al. (2005), artificial immune systems (AIS) are lacking tissue, which is present in one form or another in all living multi-cellular organisms. Some have argued that this concept in the context of AIS brings little novelty to the already saturated field of the immune inspired computational research. This article aims to show that such a component of an AIS has the potential to bring an advantage to a data processing algorithm in terms of data pre-processing, clustering and extraction of features desired by the immune inspired system. The proposed tissue algorithm is based on self-organizing networks, such as self-organizing maps (SOM) developed by Kohonen (1996) and an analogy of the so called Toll-Like Receptors (TLR) affecting the activation function of the clusters developed by the SOM.

An hr-adaptive discontinuous Galerkin method for advection-diffusion problems

We propose an adaptive mesh refinement strategy based on exploiting a combination of a pre-processing mesh re-distribution algorithm employing a harmonic mapping technique, and standard (isotropic) mesh subdivision for discontinuous Galerkin approximations of advection-diffusion problems. Numerical experiments indicate that the resulting adaptive strategy can efficiently reduce the computed discretization error by clustering the nodes in the computational mesh where the analytical solution undergoes rapid variation.