A Geometric Approach to the Problem of Unique Decomposition of Processes

This paper proposes a geometric solution to the problem of prime decomposability of concurrent processes first explored by R. Milner and F. Moller in [MM93]. Concurrent programs are given a geometric semantics using cubical areas, for which a unique factorization theorem is proved. An effective factorization method which is correct and complete with respect to the geometric semantics is derived from the factorization theorem. This algorithm is implemented in the static analyzer ALCOOL.Comment: 15 page

Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance

We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class $(\mathcal{D})$ as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows, in particular, to solve the American optimal stopping problem without having to compute the option price. Some illustrative examples based on one-dimensional diffusion processes are then provided. Another interesting application concerns the portfolio insurance. Hence, based on the ``Max-Plus martingale,'' we solve in the paper an optimization problem whose aim is to find the best martingale dominating a given floor process (on every intermediate date), w.r.t. the convex order on terminal values.Comment: Published in at http://dx.doi.org/10.1214/009117907000000222 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Design for Additive Manufacturing: A Method to Explore Unexplored Regions of the Design Space

Additive Manufacturing (AM) technologies enable the fabrication of parts and devices that are geometrically complex, have graded material compositions, and can be customized. To take advantage of these capabilities, it is important to assist designers in exploring unexplored regions of design spaces. We present a Design for Additive Manufacturing (DFAM) method that encompasses conceptual design, process selection, later design stages, and design for manufacturing. The method is based on the process-structure-property-behavior model that is common in the materials design literature. A prototype CAD system is presented that embodies the method. Manufacturable ELements (MELs) are proposed as an intermediate representation for supporting the manufacturing related aspects of the method. Examples of cellular materials are used to illustrate the DFAM method.Mechanical Engineerin

ParMooN - a modernized program package based on mapped finite elements

{\sc ParMooN} is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization for a distributed memory environment, which is the main novelty of {\sc ParMooN}. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with some parallel solvers that are available in the library {\sc PETSc}. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.Comment: partly supported by European Union (EU), Horizon 2020, Marie Sk{\l}odowska-Curie Innovative Training Networks (ITN-EID), MIMESIS, grant number 67571

Parallel load balancing strategy for Volume-of-Fluid methods on 3-D unstructured meshes

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/l Volume-of-Fluid (VOF) is one of the methods of choice to reproduce the interface motion in the simulation of multi-fluid flows. One of its main strengths is its accuracy in capturing sharp interface geometries, although requiring for it a number of geometric calculations. Under these circumstances, achieving parallel performance on current supercomputers is a must. The main obstacle for the parallelization is that the computing costs are concentrated only in the discrete elements that lie on the interface between fluids. Consequently, if the interface is not homogeneously distributed throughout the domain, standard domain decomposition (DD) strategies lead to imbalanced workload distributions. In this paper, we present a new parallelization strategy for general unstructured VOF solvers, based on a dynamic load balancing process complementary to the underlying DD. Its parallel efficiency has been analyzed and compared to the DD one using up to 1024 CPU-cores on an Intel SandyBridge based supercomputer. The results obtained on the solution of several artificially generated test cases show a speedup of up to similar to 12x with respect to the standard DD, depending on the interface size, the initial distribution and the number of parallel processes engaged. Moreover, the new parallelization strategy presented is of general purpose, therefore, it could be used to parallelize any VOF solver without requiring changes on the coupled flow solver. Finally, note that although designed for the VOF method, our approach could be easily adapted to other interface-capturing methods, such as the Level-Set, which may present similar workload imbalances. (C) 2014 Elsevier Inc. Allrights reserved.Peer ReviewedPostprint (author's final draft

Combining constructive and equational geometric constraint solving techniques

In the past few years, there has been a strong trend towards developing parametric, computer aided design systems based on geometric constraint solving. An efective way to capture the design intent in these systems is to define relationships between geometric and technological variables. In general, geometric constraint solving including functional relationships requires a general approach and appropiate techniques toachieve the expected functional capabilities. This work reports on a hybrid method which combines two geometric constraint solving techniques: Constructive and equational. The hybrid solver has the capability of managing functional relationships between dimension variables and variables representing conditions external to the geometric problem. The hybrid solver is described as a rewriting system and is shown to be correct.Postprint (published version

Automated sequence and motion planning for robotic spatial extrusion of 3D trusses

While robotic spatial extrusion has demonstrated a new and efficient means to fabricate 3D truss structures in architectural scale, a major challenge remains in automatically planning extrusion sequence and robotic motion for trusses with unconstrained topologies. This paper presents the first attempt in the field to rigorously formulate the extrusion sequence and motion planning (SAMP) problem, using a CSP encoding. Furthermore, this research proposes a new hierarchical planning framework to solve the extrusion SAMP problems that usually have a long planning horizon and 3D configuration complexity. By decoupling sequence and motion planning, the planning framework is able to efficiently solve the extrusion sequence, end-effector poses, joint configurations, and transition trajectories for spatial trusses with nonstandard topologies. This paper also presents the first detailed computation data to reveal the runtime bottleneck on solving SAMP problems, which provides insight and comparing baseline for future algorithmic development. Together with the algorithmic results, this paper also presents an open-source and modularized software implementation called Choreo that is machine-agnostic. To demonstrate the power of this algorithmic framework, three case studies, including real fabrication and simulation results, are presented.Comment: 24 pages, 16 figure

Rough differential equations driven by signals in Besov spaces

Rough differential equations are solved for signals in general Besov spaces unifying in particular the known results in H\"older and p-variation topology. To this end the paracontrolled distribution approach, which has been introduced by Gubinelli, Imkeller and Perkowski ["Paracontrolled distribution and singular PDEs", Forum of Mathematics, Pi (2015)] to analyze singular stochastic PDEs, is extended from H\"older to Besov spaces. As an application we solve stochastic differential equations driven by random functions in Besov spaces and Gaussian processes in a pathwise sense.Comment: Former title: "Rough differential equations on Besov spaces", 37 page