Code Generation for High Performance PDE Solvers on Modern Architectures

Numerical simulation with partial differential equations is an important discipline in high performance computing. Notable application areas include geosciences, fluid dynamics, solid mechanics and electromagnetics. Recent hardware developments have made it increasingly hard to achieve very good performance. This is both due to a lack of numerical algorithms suited for the hardware and efficient implementations of these algorithms not being available. Modern CPUs require a sufficiently high arithmetic intensity in order to unfold their full potential. In this thesis, we use a numerical scheme that is well-suited for this scenario: The Discontinuous Galerkin Finite Element Method on cuboid meshes can be implemented with optimal complexity exploiting the tensor product structure of basis functions and quadrature formulae using a technique called sum factorization. A matrix-free implementation of this scheme significantly lowers the memory footprint of the method and delivers a fully compute-bound algorithm. An efficient implementation of this scheme for a modern CPU requires maximum use of the processor’s SIMD units. General purpose compilers are not capable of autovectorizing traditional PDE simulation codes, requiring high performance implementations to explicitly spell out SIMD instructions. With the SIMD width increasing in the last years (reaching its current peak at 512 bits in the Intel Skylake architecture) and programming languages not providing tools to directly target SIMD units, such code suffers from a performance portability issue. This work proposes generative programming as a solution to this issue. To this end, we develop a toolchain that translates a PDE problem expressed in a domain specific language into a piece of machine-dependent, optimized C++ code. This toolchain is embedded into the existing user workflow of the DUNE project, an open source framework for the numerical solution of PDEs. Compared to other such toolchains, special emphasis is put on an intermediate representation that enables performance-oriented transformations. Furthermore, this thesis defines a new class of SIMD vectorization strategies that operate on batches of subkernels within one integration kernel. The space of these vectorization strategies is explored systematically from within the code generator in an autotuning procedure. We demonstrate the performance of our vectorization strategies and their implementation by providing measurements on the Intel Haswell and Intel Skylake architectures. We present numbers for the diffusion-reaction equation, the Stokes equations and Maxwell’s equations, achieving up to 40% of the machine’s theoretical floating point performance for an application of the DG operator

Quantum lattice models that preserve continuous translation symmetry

Bandlimited approaches to quantum field theory offer the tantalizing possibility of working with fields that are simultaneously both continuous and discrete via the Shannon Sampling Theorem from signal processing. Conflicting assumptions in general relativity and quantum field theory motivate the use of such an appealing analytical tool that could thread the needle to meet both requirements. Bandlimited continuous quantum fields are isomorphic to lattice theories, yet without requiring a fixed lattice. Any lattice with a required minimum spacing can be used. This is an isomorphism that avoids taking the limit of the lattice spacing going to zero. In this work, we explore the consequences of this isomorphism, including the emergence of effectively continuous symmetries in quantum lattice theories. One obtains conserved lattice observables for these continuous symmetries, as well as a duality of locality from the two perspectives. We expect this work and its extensions to provide useful tools for considering numerical lattice models of continuous quantum fields arising from the availability of discreteness without a fixed lattice, as well as offering new insights into emergent continuous symmetries in lattice models and possible laboratory demonstrations of these phenomena.Comment: 16 pages, 5 figure

A Novel Substrate-Based HIV-1 Protease Inhibitor Drug Resistance Mechanism

BACKGROUND: HIV protease inhibitor (PI) therapy results in the rapid selection of drug resistant viral variants harbouring one or two substitutions in the viral protease. To combat PI resistance development, two approaches have been developed. The first is to increase the level of PI in the plasma of the patient, and the second is to develop novel PI with high potency against the known PI-resistant HIV protease variants. Both approaches share the requirement for a considerable increase in the number of protease mutations to lead to clinical resistance, thereby increasing the genetic barrier. We investigated whether HIV could yet again find a way to become less susceptible to these novel inhibitors. METHODS AND FINDINGS: We have performed in vitro selection experiments using a novel PI with an increased genetic barrier (RO033-4649) and demonstrated selection of three viruses 4- to 8-fold resistant to all PI compared to wild type. These PI-resistant viruses did not have a single substitution in the viral protease. Full genomic sequencing revealed the presence of NC/p1 cleavage site substitutions in the viral Gag polyprotein (K436E and/or I437T/V) in all three resistant viruses. These changes, when introduced in a reference strain, conferred PI resistance. The mechanism leading to PI resistance is enhancement of the processing efficiency of the altered substrate by wild-type protease. Analysis of genotypic and phenotypic resistance profiles of 28,000 clinical isolates demonstrated the presence of these NC/p1 cleavage site mutations in some clinical samples (codon 431 substitutions in 13%, codon 436 substitutions in 8%, and codon 437 substitutions in 10%). Moreover, these cleavage site substitutions were highly significantly associated with reduced susceptibility to PI in clinical isolates lacking primary protease mutations. Furthermore, we used data from a clinical trial (NARVAL, ANRS 088) to demonstrate that these NC/p1 cleavage site changes are associated with virological failure during PI therapy. CONCLUSIONS: HIV can use an alternative mechanism to become resistant to PI by changing the substrate instead of the protease. Further studies are required to determine to what extent cleavage site mutations may explain virological failure during PI therapy

System Testing for PDE frameworks - tools and experiences

Testing is acknowledged as indispensible support for scientific software development and assurance of software quality to produce trustworthy simulation results. Most of the time, testing in software frameworks developed at research facilities is restricted to either unit testing or simple benchmark programs. However, in a modern numerical software framework, such as deal.II, FEniCS, or Dune, the number of possible feature combinations constituting a program is vast. Only system testing, meaning testing within a possible end user environment also emulating variability, can assess software quality and reproducibility of numerical results. We discuss tools to define system tests including both runtime and compile time variation. We furthermore discuss implementation of quality measures tailored to numerical frameworks for the solution of PDEs. We will also share experiences on using continuous integration systems (GitLab CI) for numerical software frameworks.<br><br>Poster presented at SIAM CSE17 PP108 Minisymposterium: Software Productivity and Sustainability for CSE and Data Science<br

Analysis of Mould Exposure of Immunosuppressed Patients at a German University Hospital

Moulds are ubiquitous components of outdoor and indoor air and local conditions, temperature, humidity and season can influence their concentration in the air. The impact of these factors on mould exposure in hospitals and the resulting risk of infection for low to moderately immunocompromised patients is unclear. In the present retrospective analysis for the years 2018 to 2022, the monthly determined mould contamination of the outdoor and indoor air at the University Hospital Frankfurt am Main is compared with the average air temperature and the relative humidity. Mould infections (Aspergillus spp., Mucorales) of low to moderately immunosuppressed patients of a haematological-oncological normal ward were determined clinically according to the criteria of the European Organisation for Research and Treatment of Cancer (EORTC, Brussels, Belgium) and of the National Reference Centre for Surveillance of Nosocomial Infections (NRC-NI, Berlin, Germany). The data revealed that in the summer months (May–October), increased mould contamination was detectable in the outdoor and indoor air compared to the winter months (November–April). The mould levels in the patient rooms followed the detection rates of the outdoor air. Two nosocomial Aspergillus infections, one nosocomial Mucorales (Rhizopus spp.) infection (according to both NRC-NI and EORTC criteria) and five Aspergillus spp. infections (according to EORTC criteria) occurred in 4299 treated patients (resulting in 41,500 patient days). In our study, the incidence density rate of contracting a nosocomial mould infection (n = 3) was approximately 0.07 per 1000 patient days and appears to be negligible

The Distributed and Unified Numerics Environment, Version 2.4

The Dune project has released version 2.4 on September 25, 2015. This paper describes the most significant improvements, interface and other changes for the Dune core modules Dune- Common, Dune-Geometry, Dune-Grid, Dune-ISTL, and Dune-LocalFunctions

Joint Europa Mission (JEM): A Multiscale, Multi-Platform Mission to Characterize Europa's Habitability and Search for Extant Life. A White Paper prepared for the NAS 2023-2032 Decadal Survey for Planetary Science and Astrobiology August 15th, 2020

International audienceIn this White Paper we propose that NASA works with ESA and other potentially interested international partners to design and fly jointly an ambitious and exciting planetary mission to characterize Europa's habitability and search for bio-signatures in the environment of Europa (surface, subsurface and exosphere). A White Paper prepared for the NAS 2023-2032 Decadal Survey for Planetary Science and Astrobiology August 15th, 202