Marcin Sieniek

Application of multi-agent paradigm to hp-adaptive projection-based interpolation operator

Abstract In this paper we discuss applications and design of the agent-based, hp-adaptive projection-based interpolation (PBI) operator. We describe the use of mesh adaptation process to produce a faithful representation of an input image in the Finite Element (FE) space. This can be used, in turn, to generate from the input bitmap continuous material functions required for further FE computations. We propose an agent-based architecture suitable for localized implementation of the PBI operator. Finally, we show how to apply it to an exemplary problem of austenite–ferrite phase transformation.

Two-dimensional HP-adaptive Algorithm for Continuous Approximations of Material Data Using Space Projection

In this paper we utilize the concept of the L 2 and H 1 projections used to adaptively generate a continuous approximation of an input material data in the finite element (FE) base. This approximation, along with a corresponding FE mesh, can be used as material data for FE solvers. We begin with a brief theoretical background, followed by description of the hp-adaptive algorithm adopted here to improve gradually quality of the projections. We investigate also a few distinct sample problems, apply the aforementioned algorithms and conclude with numerical results evaluation.

Employing an Adaptive Projection-based Interpolation to Prepare Discontinuous 3D Material Data for Finite Element Analysis☆

Abstract In this paper we propose an adaptive 3D image data pre-processing technique for generating a continuous approximation of an input image representing some material data, along with a finite element mesh aligned to the properties of the material, which can be used as the initial mesh for a further hp-adaptive finite element analysis. First, we introduce the projection-based interpolation operator, we explain some design considerations, useful for reproducing this work, then we present a benchmark problem used as a proof of concept and we conclude with numerical results for this exemplary problem, obtained with our implementation of the discussed method.

Agent-based parallel system for numerical computations

Abstract The paper describes a way of applying agent paradigm to hp-adaptive Finite Element Method (hp-FEM). We discuss a choice of classical numerical algorithms suitable for incorporating into an agent-based application, along with an efficient way of adopting them into an agent-based application. We define formally a Computing Multi Agent System (C-MAS) for adaptive 1D FEM based on Smart Solid Agent model and describe tasks executed by hp-FEM agents. Finally, we spare a few paragraphs for numerical experiments performed with an application developed accordingly to the described model.

Agent-oriented image processing with the hp-adaptive projection-based interpolation operator

In this paper we discuss applications and design of the agent-oriented, hp-adaptive projection-based interpolation technique. We describe the use of the mesh adaptation process to produce the most faithful representation of the input image in the Finite Element space. We discuss the advantages of the agent-oriented application model both in general and in terms of the hp-adaptive application properties. Lastly, we describe a sample problem used as a proof of concept.

Employing Adaptive Finite Elements to Model Squeezing of a Layered Material in 3D

Finite element method (FEM) has long been an important tool for modeling a variety of processes including applications in mechanics [1], material science [2], [3], geology [4]-[6] and nanoengineering [7]. The hp-FEM is the most sophisticated version of the mesh adaptive algorithms [1], where elements are automatically h-refined (broken into smaller elements) or p-refined (polynomial order of approximating base is increased over selected elements). The decisions about finite elements that need to be refined are made iteratively based on the a posteriori error decrease estimate.

Unified Modeling Language description of the object-oriented multi-scale adaptive finite element method for Step-and-Flash Imprint Lithography Simulations

In the first part of the paper we present the multi-scale simulation of the Step-and-Flash Imprint Lithography (SFIL), a modern patterning process. The simulation utilizes the hp adaptive Finite Element Method (hp-FEM) coupled with Molecular Statics (MS) model. Thus, we consider the multi-scale problem, with molecular statics applied in the areas of the mesh where the highest accuracy is required, and the continuous linear elasticity with thermal expansion coefficient applied in the remaining part of the domain. The degrees of freedom from macro-scale elements nodes located on the macro-scale side of the interface have been identified with particles from nano-scale elements located on the nano-scale side of the interface. In the second part of the paper we present Unified Modeling Language (UML) description of the resulting multi-scale application (hp-FEM coupled with MS). We investigated classical, procedural codes from the point of view of the object-oriented (O-O) programming paradigm. The discovered hierarchical structure of classes and algorithms makes the UML project as independent on the spatial dimension of the problem as possible. The O-O UML project was defined at an abstract level, independent on the programming language used.

Fast Graph Transformation based Direct Solver Algorithm for Regular Three Dimensional Grids

Abstract This paper presents a graph-transformation-based multifrontal direct solver with an optimization technique that allows for a significant decrease of time complexity in some multi-scale simulations of the Step and Flash Imprint Lithography (SFIL). The multi-scale simulation consists of a macro-scale linear e lasticity model with thermal expansion coefficient and a nano-scale molecular statics model. The algorithm is exemplified with a photopolimerization simulation that involves densification of a polymer inside a feature followed by shrinkage of the feature after removal of the template. The solver is optimized thanks to a mechanism of reusing sub -domains with similar geometries and similar material properties. The graph transformation formalism is used to describe the algorithm - such an approach helps automatically localize sub-domains that can be reused.

Hypergraph Grammar based Adaptive Linear Computational Cost Projection Solvers for Two and Three Dimensional Modeling of Brain

Abstract In this paper we present a hypergraph grammar model for transformation of two and three dimensional grids. The hypergraph grammar concerns the proces of generation of uniform grids with two or three dimensional rectangular or hexahedral elements, followed by the proces of h refinements, namely breaking selected elements into four or eight son elements, in two or three dimensions, respectively. The hypergraph grammar presented in this paper expresses also the two solver algorithms. The first one is the projection based interpolation solver algorithm used for computing H1 or L2 projections of MRI scan of human head, in two and three dimensions. The second one is the multi-frontal direct solver utilized in the loop of the Euler scheme for solving the non-stationary problem modeling the three dimensional heat transport in the human head generated by the cellphone usage.

Agent-based Algorithm for Spatial Distribution of Objects

Abstract In this paper we present an agent-based algorithm for the spatial distribution of objects. The algorithm is a generalization of the bubble mesh algorithm, initially created for the point insertion stage of the meshing process of the finite element method. The bubble mesh algorithm treats objects in space as bubbles, which repel and attract each other. The dynamics of each bubble are approximated by solving a series of ordinary differential equations. We present numerical results for a meshing application as well as a graph visualization application.