Towards exascale BEM simulations: hybrid parallelisation strategies for boundary element methods

Many fields of engineering benefit from an accurate and reliable solver for the Laplace equation. Such an equation is able to model many different phenomena, and is at the base of several multi-physics solvers. For example, in nautical engineering, since the Navier{Stokes system has an extremely high computational cost, many reduced order models are often used to predict ship performance. Under the assumption of incompressible fluid and irrotational flow it is possible to recover a flow field by simply imposing mass conservation, which simplifies to a Laplace equation. Morevore, the deep theoretical background that surrounds this equation, makes it ideal as a benchmark to test new numerical softwares. Over the last decades such equation has often been solved through its Boundary integral formulation, leading to Boundary Element Methods. What makes such methods appealing with respect to a classical Finite Element Method is the fact that they only require discretisation of the boundary. The purpose of the present work is to develop an effcient and optimize BEM for the Laplace equation, designed around the architecture of modern CPUs

The deal.II Library, Version 8.5

This paper provides an overview of the new features of the finite element library deal.II version 8.5

The deal.II Library, Version 9.1

This paper provides an overview of the new features of the finite element library deal.II, version 9.1

The deal.II Library, Version 9.0

This paper provides an overview of the new features of the finite element library deal.II version 9.0

The Peano software---parallel, automaton-based, dynamically adaptive grid traversals

We discuss the design decisions, design alternatives, and rationale behind the third generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from spacetrees. Peano ties the mesh traversal to the mesh storage and supports only one element-wise traversal order resulting from space-filling curves. The user is not free to choose a traversal order herself. The traversal can exploit regular grid subregions and shared memory as well as distributed memory systems with almost no modifications to a serial application code. We formalize the software design by means of two interacting automata—one automaton for the multiscale grid traversal and one for the application-specific algorithmic steps. This yields a callback-based programming paradigm. We further sketch the supported application types and the two data storage schemes realized before we detail high-performance computing aspects and lessons learned. Special emphasis is put on observations regarding the used programming idioms and algorithmic concepts. This transforms our report from a “one way to implement things” code description into a generic discussion and summary of some alternatives, rationale, and design decisions to be made for any tree-based adaptive mesh refinement software

Extension of the -BEM library for use in a seakeeping pipeline

The problem of seakeeping consists, among other aspects, of studying how a ship reacts to the environmental conditions during navigation, to establish operational limits and verify the seaworthiness of the vessel. A classic approach is to model the ship as a filter, with a set of Response Amplitude Operators (RAO) transforming the wave elevation time series into the motions in the six degrees of freedom. Thanks to the convolutional properties of the Fast Fourier Transform, a wave elevation time series can then be converted to the prediction of ship motions in real time. For different ship speeds, wave directions and wave frequencies, the RAOs can be determined from the added masses, damping and hydrostatic coefficients, and wave-induced forces and moments. These entities can be obtained from the solutions of suitable complex-valued potential flow problems, in an offline phase. This work, developed as part of the Winning a Sea State project in collaboration with Cetena, illustrates the extension of the potential flow solver -BEM to support these formulations, in order to provide an efficient, scalable, open source basis for a pipeline of this type. Results for the added mass and damping coefficients of a semi-submerged sphere in the zero-speed case compare favorably with the theory

Multidimensional rank-one convexification of incremental damage models at finite strains

This paper presents computationally feasible rank-one relaxation algorithms for the efficient simulation of a time-incremental damage model with nonconvex incremental stress potentials in multiple spatial dimensions. While the standard model suffers from numerical issues due to the lack of convexity, the relaxation techniques circumvent the problem of non-existence of minimizers and prevent mesh dependency of the solutions of discretized boundary value problems using finite elements. By the combination, modification and parallelization of the underlying convexification algorithms the approach becomes computationally feasible. A descent method and a Newton scheme enhanced by step size control strategies prevents stability issues related to local minima in the energy landscape and the computation of derivatives. Special techniques for the construction of continuous derivatives of the approximated rank-one convex envelope are discussed. A series of numerical experiments demonstrates the ability of the computationally relaxed model to capture softening effects and the mesh independence of the computed approximations