Abstract: Christopher T. Lee, John B. Moody, Rommie E. Amaro, J. Andrew Mccammon, Michael J. Holst

We introduce the Colored Simplicial Complex library (CASC): a new, modern, and header-only C++ library that provides a data structure to represent arbitrary dimension abstract simplicial complexes (ASC) with user-defined classes stored directly on the simplices at each dimension. This is accomplished by using the latest C++ language features including variadic template parameters introduced in C++11 and automatic function return type deduction from C++14. Effectively, CASC decouples the representation of the topology from the interactions of user data. We present the innovations and design principles of the data structure and related algorithms. This includes a metadata-aware decimation algorithm, which is general for collapsing simplices of any dimension. PubDate: Thu, 08 Aug 2019 00:00:00 GMT

We present an algorithmic framework for matrix-free evaluation of discontinuous Galerkin finite element operators. It relies on fast quadrature with sum factorization on quadrilateral and hexahedral meshes, targeting general weak forms of linear and nonlinear partial differential equations. Different algorithms and data structures are compared in an in-depth performance analysis. The implementations of the local integrals are optimized by vectorization over several cells and faces and an even-odd decomposition of the one-dimensional interpolations. Up to 60% of the arithmetic peak on Intel Haswell, Broadwell, and Knights Landing processors is reached when running from caches and up to 40% of peak when also considering the access to vectors from main memory. PubDate: Thu, 08 Aug 2019 00:00:00 GMT

We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions 0F1, 1F1, 2F1, and 2F0 (or the Kummer U-function) are supported for unrestricted complex parameters and argument, and, by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, Airy functions, Legendre functions, Jacobi polynomials, complete elliptic integrals, and other special functions. The output can be used directly for interval computations or to generate provably correct floating-point approximations in any format. Performance is competitive with earlier arbitrary-precision software and sometimes orders of magnitude faster. PubDate: Thu, 08 Aug 2019 00:00:00 GMT

Abstract: Adrián P. Diéguez, Margarita Amor, Ramón Doallo

Solving tridiagonal linear-equation systems is a fundamental computing kernel in a wide range of scientific and engineering applications, and its computation can be modeled with parallel algorithms. These parallel solvers are typically designed to compute problems whose data fit in a common shared-memory space where all the cores taking part in the computation have access. However, when the problem size is large, data cannot be entirely stored in the common shared-memory space, and a high number of high-latency communications are performed. One alternative is to partition the problem among different memory spaces. At this point, conventional parallel algorithms do not facilitate the partition of computation in independent tiles, since each reduction depends on equations that may be in different tiles. PubDate: Thu, 08 Aug 2019 00:00:00 GMT

Abstract: Coralia Cartis, Jan Fiala, Benjamin Marteau, Lindon Roberts

We present two software packages for derivative-free optimization (DFO): DFO-LS for nonlinear least-squares problems and Py-BOBYQA for general objectives, both with optional bound constraints. Inspired by the Gauss-Newton method, DFO-LS constructs simplified linear regression models for the residuals and allows flexible initialization for expensive problems, whereby it can begin making progress after as few as two objective evaluations. Numerical results show DFO-LS can gain reasonable progress on some medium-scale problems with fewer objective evaluations than is needed for one gradient evaluation. DFO-LS has improved robustness to noise, allowing sample averaging, regression-based model construction, and multiple restart strategies with an auto-detection mechanism. PubDate: Thu, 08 Aug 2019 00:00:00 GMT

In this article, we present the Python framework pySDC for solving collocation problems with spectral deferred correction (SDC) methods and their time-parallel variant PFASST, the parallel full approximation scheme in space and time. pySDC features many implementations of SDC and PFASST, from simple implicit timestepping to high-order implicit-explicit or multi-implicit splitting and multilevel SDCs. The software package comes with many different, preimplemented examples and has seven tutorials to help new users with their first steps. Time parallelism is implemented either in an emulated way for debugging and prototyping or using MPI for benchmarking. The code is fully documented and tested using continuous integration, including most results of previous publications. PubDate: Thu, 08 Aug 2019 00:00:00 GMT

Abstract: Cristiano M. Agulhari, Alexandre Felipe, Ricardo C. L. F. Oliveira, Pedro L. D. Peres

The ROLMIP (Robust LMI Parser) is a toolbox specialized in control theory for uncertain linear systems, built to work under MATLAB jointly with YALMIP, to ease the programming of sufficient Linear Matrix Inequality (LMI) conditions that, if feasible, assure the validity of parameter-dependent LMIs in the entire set of uncertainty considered. This article presents the new version of the ROLMIP toolbox, which was completely remodeled to provide a high-level user-friendly interface to cope with distinct uncertain domains (hypercube and multi-simplex) and to treat time-varying parameters in discrete- and continuous-time. By means of simple commands, the user is able to define polynomial matrices as well as to describe the desired parameter-dependent LMIs in an easy way, considerably reducing the programming time to end up with implementable LMI conditions. PubDate: Thu, 08 Aug 2019 00:00:00 GMT

Abstract: Armando Faz-Hernández, Julio López, Ricardo Dahab

Elliptic curve cryptosystems are considered an efficient alternative to conventional systems such as DSA and RSA. Recently, Montgomery and Edwards elliptic curves have been used to implement cryptosystems. In particular, the elliptic curves Curve25519 and Curve448 were used for instantiating Diffie-Hellman protocols named X25519 and X448. Mapping these curves to twisted Edwards curves allowed deriving two new signature instances, called Ed25519 and Ed448, of the Edwards Digital Signature Algorithm. In this work, we focus on the secure and efficient software implementation of these algorithms using SIMD parallel processing. We present software techniques that target the Intel AVX2 vector instruction set for accelerating prime field arithmetic and elliptic curve operations. PubDate: Tue, 30 Jul 2019 00:00:00 GMT

Adjoint methods have become fundamental ingredients of the scientific computing toolbox over the past decades. Large-scale parameter sensitivity analysis, uncertainty quantification, and nonlinear optimization would otherwise turn out computationally infeasible. The symbolic derivation of adjoint mathematical models for relevant problems in science and engineering and their implementation in consistency with the implementation of the underlying primal model frequently proves highly challenging. Hence, an increased interest in algorithmic adjoints can be observed. The algorithmic derivation of adjoint numerical simulation programs shifts some of the problems faced from functional and numerical analysis to computer science. It becomes a highly complex software engineering task requiring expertise in software analysis, transformation, and optimization. PubDate: Tue, 30 Jul 2019 00:00:00 GMT

We consider the problem of computing rigorous enclosures for polynomials represented in the Chebyshev basis. Our aim is to compare and develop algorithms with a linear complexity in terms of the polynomial degree. A first category of methods relies on a direct interval evaluation of the given Chebyshev expansion in which Chebyshev polynomials are bounded, e.g., with a divide-and-conquer strategy. Our main category of methods that are based on the Clenshaw recurrence includes interval Clenshaw with defect correction (ICDC), and the spectral transformation of Clenshaw recurrence rewritten as a discrete dynamical system. An extension of the barycentric representation to interval arithmetic is also considered that has a log-linear complexity as it takes advantage of a verified discrete cosine transform. PubDate: Tue, 30 Jul 2019 00:00:00 GMT

The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box, and complementarity (BBC) constraints. Given a POP in the class and a relaxation order, BBCPOP constructs a simple conic optimization problem (COP), which serves as a doubly nonnegative relaxation of the POP, and then solves the COP by applying the bisection and projection method. The COP is expressed with a linear objective function and constraints described as a single hyperplane and two cones, which are the Cartesian product of positive semidefinite cones and a polyhedral cone induced from the BBC constraints. PubDate: Tue, 30 Jul 2019 00:00:00 GMT

A bottom-up approach to parallel anisotropic mesh generation is presented by building a mesh generator starting from the basic operations of vertex insertion and Delaunay triangles. Applications focusing on high-lift design or dynamic stall, or numerical methods and modeling test cases, still focus on two-dimensional domains. This automated parallel mesh generation approach can generate high-fidelity unstructured meshes with anisotropic boundary layers for use in the computational fluid dynamics field. The anisotropy requirement adds a level of complexity to a parallel meshing algorithm by making computation depend on the local alignment of elements, which in turn is dictated by geometric boundaries and the density functions— one-dimensional spacing functions generated from an exponential distribution. PubDate: Thu, 18 Jul 2019 00:00:00 GMT