Parallel Multiscale Contact Dynamics for Rigid Non-spherical Bodies

The simulation of large numbers of rigid bodies of non-analytical shapes or vastly varying sizes which collide with each other is computationally challenging. The fundamental problem is the identification of all contact points between all particles at every time step. In the Discrete Element Method (DEM), this is particularly difficult for particles of arbitrary geometry that exhibit sharp features (e.g. rock granulates). While most codes avoid non-spherical or non-analytical shapes due to the computational complexity, we introduce an iterative-based contact detection method for triangulated geometries. The new method is an improvement over a naive brute force approach which checks all possible geometric constellations of contact and thus exhibits a lot of execution branching. Our iterative approach has limited branching and high floating point operations per processed byte. It thus is suitable for modern Single Instruction Multiple Data (SIMD) CPU hardware. As only the naive brute force approach is robust and always yields a correct solution, we propose a hybrid solution that combines the best of the two worlds to produce fast and robust contacts. In terms of the DEM workflow, we furthermore propose a multilevel tree-based data structure strategy that holds all particles in the domain on multiple scales in grids. Grids reduce the total computational complexity of the simulation. The data structure is combined with the DEM phases to form a single touch tree-based traversal that identifies both contact points between particle pairs and introduces concurrency to the system during particle comparisons in one multiscale grid sweep. Finally, a reluctant adaptivity variant is introduced which enables us to realise an improved time stepping scheme with larger time steps than standard adaptivity while we still minimise the grid administration overhead. Four different parallelisation strategies that exploit multicore architectures are discussed for the triad of methodological ingredients. Each parallelisation scheme exhibits unique behaviour depending on the grid and particle geometry at hand. The fusion of them into a task-based parallelisation workflow yields promising speedups. Our work shows that new computer architecture can push the boundary of DEM computability but this is only possible if the right data structures and algorithms are chosen

Generating Distributed Programs from Event-B Models

Distributed algorithms offer challenges in checking that they meet their specifications. Verification techniques can be extended to deal with the verification of safety properties of distributed algorithms. In this paper, we present an approach for combining correct-by-construction approaches and transformations of formal models (Event-B) into programs (DistAlgo) to address the design of verified distributed programs. We define a subset LB (Local Event-B) of the Event-B modelling language restricted to events modelling the classical actions of distributed programs as internal or local computations, sending messages and receiving messages. We define then transformations of the various elements of the LB language into DistAlgo programs. The general methodology consists in starting from a statement of the problem to program and then progressively producing an LB model obtained after several refinement steps of the initial LB model. The derivation of the LB model is not described in the current paper and has already been addressed in other works. The transformation of LB models into DistAlgo programs is illustrated through a simple example. The refinement process and the soundness of the transformation allow one to produce correct-by-construction distributed programs.Comment: In Proceedings VPT/HCVS 2020, arXiv:2008.0248

Refinement Modal Logic

In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition to the standard modalities 'box' for each agent. The operator 'all' acts as a quantifier over the set of all refinements of a given model. As a variation on a bisimulation quantifier, this refinement operator or refinement quantifier 'all' can be seen as quantifying over a variable not occurring in the formula bound by it. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second-order quantification. We present a sound and complete axiomatization of multi-agent refinement modal logic. We also present an extension of the logic to the modal mu-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be seen as a set of actions), and to dynamic epistemic logic. We further give detailed results on the complexity of satisfiability, and on succinctness

The Grid Sketcher: An AutoCad-based tool for conceptual design processes

Sketching with pencil and paper is reminiscent of the varied, rich, and loosely defined formal processes associated with conceptual design. Architects actively engage such creative paradigms in their exploration and development of conceptual design solutions. The Grid Sketcher, as a conceptual sketching tool, presents one possible computer implementation for enhancing and supporting these processes. It effectively demonstrates the facility with which current technology and the computing environment can enhance and simulate sketching intents and expectations; Typically with respect to design, the position taken is that the two are virtually void of any fundamental commonality. A designer\u27s thoughts are intuitive, at times irrational, and rarely follow consistently identifiable patterns. Conversely, computing requires predictability in just these endeavors. The computing environment, as commonly defined, can not reasonably expect to mimic the typically human domain of creative design. In this context, this thesis accentuates the computer\u27s role as a form generator as opposed to a form evaluator. The computer, under the influence of certain contextual parameters can, however, provide the designer with a rich and elegant set of forms that respond through algorithmics to the designer\u27s creative intents. (Abstract shortened by UMI.)