arXiv subjects

Tobias Weinzierl

Publications and source records attributed to Tobias Weinzierl.

At least 19 recordsLinked to original sources

arXiv2026

DSLHyPE-a DSL kernel language for the Exascale Hyperbolic PDE Engine ExaHyPE

We introduce a bilingual domain-specific language (DSL) for modelling compute kernels within a generic solver for hyperbolic partial differential equations (PDEs). Users express PDE terms, i.e.~the underlying physics, in a familiar native language such as C or C++, while the numerical scheme is specified in a Python-embedded DSL, DSLHyPE. DSLHyPE's compiler lowers the Python description to MLIR and introduces a translation pass that integrates it with native code likewise mapped to MLIR. Our approach keeps the numerical representation and the physics implementation separate for as long as possible, while delegating optimization to the compiler through existing MLIR optimization passes. This separation of concerns benefits researchers developing numerical schemes on top of existing PDE implementations or with applications involving nonlinear systems whose PDE terms must solve PDEs themselves. We demonstrate the feasibility of the approach using a gravitational-wave solver and a matter-evolution solver on x86 processors and H200 GPUs.

cs.MS↗

arXiv2026

Memory Layouts for GPU-Data Transfer Buffering in SPH

The rise in GPU compute speed has outpaced improvements in host-to-device memory transfer speeds, despite the advent of shared-memory superchips. Consequently, memory transfer times now constitute an increasingly large fraction of total time-to-solution, compelling developers to compress GPU kernel input and output data into compact, minimal formats prior to GPU-offloading. This complements existing work on GPU- and compute-friendly data arrangements. We study a Smoothed Particle Hydrodynamics solver and propose memory layout strategies for host-side particle data that are particularly well-suited to GPU-offloading. Specifically, we advocate splitting classic array-of-struct data structures into a split array-of-struct arrangement, in which each logical struct decomposes into substructs determined by kernel read/write access patterns and attribute types. Splitting a monolithic particle struct into several bespoke, finer-grained structs can reduce the time required to pack data to and from buffers by ~20% - 40%, lowering total time spent on GPU-offloading by ~12% - 25%.

cs.DC↗

arXiv2026

Task-parallelism in SWIFT for heterogeneous compute architectures

This paper highlights first steps towards enabling graphics processing unit (GPU) acceleration of the task-parallel smoothed particle hydrodynamics (SPH) solver SWIFT. Novel combinations of algorithms are presented, enabling SWIFT to function as a truly heterogeneous software leveraging task-parallelism on CPUs for memory-bound computations concurrently with GPUs for compute-bound computations while minimising the effects of CPU-GPU communication latency. The proposed algorithms are validated in extensive testing. The GPU acceleration methodology is shown to deliver up to 3.5 and 7.5 speedups for the offloaded computations when including and excluding the time required to prepare and post-process data transfers on the CPU side, respectively. The overall performance of the GPU-accelerated hydrodynamic solver for a full simulation on a single Grace-Hopper superchip is 1.8 times faster compared to the superchips fully parallelised CPU capabilities. This constitutes an improvement from 8 million particle updates/s for the full CPU-only baseline (115,000 updates per CPU core) to 15 million updates/s for the GPU-accelerated SPH solver. Moreover, it displays near-perfect strong scaling on 4 Grace-Hopper nodes. The GPU-acceleration is also demonstrated to give a 29 percent improvement in energy efficiency in comparison to CPU-only baselines. Finally, inter-influential bottlenecks in the prototype solver presented in this work are identified: A significant amount of time (up to 80 percent) of a GPU-offloading cycle is spent on preparing and post-processing particle data on the CPU for the transfer to and from the GPU, respectively. Approaches are suggested to minimise their effects and maximise the solver's performance in our future work.

cs.PF↗

arXiv2025

An extension of C++ with memory-centric specifications for HPC to reduce memory footprints and streamline MPI development

C++ leans towards a memory-inefficient storage of structs: The compiler inserts padding bits, while it is not able to exploit knowledge about the range of integers, enums or bitsets. Furthermore, the language provides no support for arbitrary floating-point precisions. We propose a language extension based upon attributes through which developers can guide the compiler what memory arrangements would be beneficial: Can multiple booleans or integers with limited range be squeezed into one bit field, do floating-point numbers hold fewer significant bits than in the IEEE standard, and is a programmer willing to trade attribute ordering guarantees for a more compact object representation? The extension offers the opportunity to fall back to normal alignment and native C++ floating point representations via plain C++ assignments, no dependencies upon external libraries are introduced, and the resulting code remains (syntactically) standard C++. As MPI remains the de-facto standard for distributed memory calculations in C++, we furthermore propose additional attributes which streamline the MPI datatype modelling in combination with our memory optimisation extensions. Our work implements the language annotations within LLVM and demonstrates their potential impact through smoothed particle hydrodynamics benchmarks. They uncover the potential gains in terms of performance and development productivity.

cs.MS↗

arXiv2025

Compiler-supported reduced precision and AoS-SoA transformations for heterogeneous hardware

This study evaluates AoS-to-SoA transformations over reduced-precision data layouts for a particle simulation code on several GPU platforms: We hypothesize that SoA fits particularly well to SIMT, while AoS is the preferred storage format for many Lagrangian codes. Reduced-precision (below IEEE accuracy) is an established tool to address bandwidth constraints, although it remains unclear whether AoS and precision conversions should execute on a CPU or be deployed to a GPU if the compute kernel itself must run on an accelerator. On modern superchips where CPUs and GPUs share (logically) one data space, it is also unclear whether it is advantageous to stream data to the accelerator prior to the calculation, or whether we should let the accelerator transform data on demand, i.e.~work in-place logically. We therefore introduce compiler annotations to facilitate such conversions and to give the programmer the option to orchestrate the conversions in combination with GPU offloading. For some of our compute kernels of interest, Nvidia's G200 platforms yield a speedup of around 2.6 while AMD's MI300A exhibits more robust performance yet profits less. We assume that our compiler-based techniques are applicable to a wide variety of Lagrangian codes and beyond.

cs.PL↗

arXiv2025

Implementation techniques for multigrid solvers for high-order Discontinuous Galerkin methods

Matrix-free geometric multigrid solvers for elliptic PDEs that have been discretised with Higher-order Discontinuous Galerkin (DG) methods are ideally suited to exploit state-of-the-art computer architectures. Higher polynomial degrees offer exponential convergence, while the workload fits to vector units, is straightforward to parallelise, and exhibits high arithmetic intensity. Yet, DG methods such as the interior penalty DG discreisation do not magically guarantee high performance: they require non-local memory access due to coupling between neighbouring cells and break down into compute steps of widely varying costs and compute character. We address these limitations by developing efficient execution strategies for $hp$-multigrid. Separating cell- and facet-operations by introducing auxiliary facet variables localizes data access, reduces the need for frequent synchronization, and enables overlap of computation and communication. Loop fusion results in a single-touch scheme which reads (cell) data only once per smoothing step. We interpret the resulting execution strategies in the context of a task formalism, which exposes additional concurreny. The target audience of this paper are practitioners in Scientific Computing who are not necessarily experts on multigrid or familiar with sophisticated discretisation techniques. By discussing implementation techniques for a powerful solver algorithm we aim to make it accessible to the wider community.

math.NA↗

arXiv2025

Annotation-guided AoS-to-SoA conversions and GPU offloading with data views in C++

The C++ programming language provides classes and structs as fundamental modeling entities. Consequently, C++ code tends to favour array-of-structs (AoS) for encoding data sequences, even though structure-of-arrays (SoA) yields better performance for some calculations. We propose a C++ language extension based on attributes that allows developers to guide the compiler in selecting memory arrangements, i.e.~to select the optimal choice between AoS and SoA dynamically depending on both the execution context and algorithm step. The compiler can then automatically convert data into the preferred format prior to the calculations and convert results back afterward. The compiler handles all the complexity of determining which data to convert and how to manage data transformations. Our implementation realises the compiler-extension for the new annotations in Clang and demonstrates their effectiveness through a smoothed particle hydrodynamics (SPH) code, which we evaluate on an Intel CPU, an ARM CPU, and a Grace-Hopper GPU. While the separation of concerns between data structure and operators is elegant and provides performance improvements, the new annotations do not eliminate the need for performance engineering. Instead, they challenge conventional performance wisdom and necessitate rethinking approaches how to write efficient implementations.

cs.MS↗

arXiv2025

Fast Higher-Order Interpolation and Restriction in ExaHyPE Avoiding Non-physical Reflections

Wave equations help us to understand phenomena ranging from earthquakes to tsunamis. These phenomena materialise over very large scales. It would be computationally infeasible to track them over a regular mesh. Yet, since the phenomena are localised, adaptive mesh refinement (AMR) can be used to construct meshes with a higher resolution close to the regions of interest. ExaHyPE is a software engine created to solve wave problems using AMR, and we use it as baseline to construct our numerical relativity application called ExaGRyPE. To advance the mesh in time, we have to interpolate and restrict along resolution transitions in each and every time step. ExaHyPE's vanilla code version uses a d-linear tensor-product approach. In benchmarks of a stationary black hole this performs slowly and leads to errors in conserved quantities near AMR boundaries. We therefore introduce a set of higher-order interpolation schemes where the derivatives are calculated at each coarse grid cell to approximate the enclosed fine cells. The resulting methods run faster than the tensor-product approach. Most importantly, when running the stationary black hole simulation using the higher order methods the errors near the AMR boundaries are removed.

cs.CE↗

arXiv2024

ExaGRyPE: Numerical General Relativity Solvers Based upon the Hyperbolic PDEs Solver Engine ExaHyPE

ExaGRyPE describes a suite of solvers for numerical relativity, based upon ExaHyPE 2, the second generation of our Exascale Hyperbolic PDE Engine. The presented generation of ExaGRyPE solves the Einstein equations in the CCZ4 formulation under a 3+1 foliation and focuses on black hole spacetimes. It employs a block-structured Cartesian grid carrying a higher-order order Finite Difference scheme with adaptive mesh refinement, it facilitates massive parallelism combining message passing, domain decomposition and task parallelism, and it supports the injection of particles into the grid as data probes or tracers. We introduce the ExaGRyPE-specific building blocks within ExaHyPE 2, and discuss its software architecture and compute-n-feel: For this, we formalize the creation of any specific simulation with ExaGRyPE as a sequence of lowering operations, where abstract logical tasks are successively broken into finer tasks until we obtain an abstraction level that can be mapped onto a C++ executable. The overall program logic is fully specified via a domain-specific Python interface, we map this logic onto a more detailed set of numerical tasks, subsequently lower this representation onto technical tasks that the underlying ExaHyPE engine uses to parallelize the application, before eventually the technical tasks are mapped onto task graphs including the actual PDE term evaluations, initial conditions, boundary conditions, and so forth. We end up with a rigorous separation of concerns which shields ExaGRyPE users from technical details and hence simplifies the development of novel physical models. We present the simulations and data for the gauge wave, static single black holes and rotating binary black hole systems, demonstrating that the code base is mature and usable. However, we also uncover domain-specific numerical challenges that need further study by the community in future work.

gr-qc↗

arXiv2024

Compiler support for semi-manual AoS-to-SoA conversions with data views

The C programming language and its cousins such as C++ stipulate the static storage of sets of structured data: Developers have to commit to one, invariant data model -- typically a structure-of-arrays (SoA) or an array-of-structs (AoS) -- unless they manually rearrange, i.e.~convert it throughout the computation. Whether AoS or SoA is favourable depends on the execution context and algorithm step. We propose a language extension based upon C++ attributes through which developers can guide the compiler what memory arrangements are to be used. The compiler can then automatically convert (parts of) the data into the format of choice prior to a calculation and convert results back afterwards. As all conversions are merely annotations, it is straightforward for the developer to experiment with different storage formats and to pick subsets of data that are subject to memory rearrangements. Our work implements the annotations within Clang and demonstrates their potential impact through a smoothed particle hydrodynamics (SPH) code.

cs.PL↗

arXiv2024

Detrimental task execution patterns in mainstream OpenMP runtimes

The OpenMP API offers both task-based and data-parallel concepts to scientific computing. While it provides descriptive and prescriptive annotations, it is in many places deliberately unspecific how to implement its annotations. As the predominant OpenMP implementations share design rationales, they introduce "quasi-standards how certain annotations behave. By means of a task-based astrophysical simulation code, we highlight situations where this "quasi-standard" reference behaviour introduces performance flaws. Therefore, we propose prescriptive clauses to constrain the OpenMP implementations. Simulated task traces uncover the clauses' potential, while a discussion of their realization highlights that they would manifest in rather incremental changes to any OpenMP runtime supporting task priorities.

cs.PL↗

arXiv2023

SYCL compute kernels for ExaHyPE

We discuss three SYCL realisations of a simple Finite Volume scheme over multiple Cartesian patches. The realisation flavours differ in the way how they map the compute steps onto loops and tasks: We compare an implementation that is exclusively using a sequence of for-loops to a version that uses nested parallelism, and finally benchmark these against a version modelling the calculations as task graph. Our work proposes realisation idioms to realise these flavours within SYCL. The results suggest that a mixture of classic task and data parallelism performs if we map this hybrid onto a solely data-parallel SYCL implementation, taking into account SYCL specifics and the problem size.

cs.MS↗

arXiv2023

Parallel local time stepping for rigid bodies represented by triangulated meshes

Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost instantaneously due to collisions. Dense particle packings hence require tiny time step sizes, while free particles can advance with large time steps. Admissible time step sizes can span multiple orders of magnitudes. We propose an adaptive local time stepping algorithm which identifies clusters of particles that can be updated independently, advances them optimistically and independently in time, determines collision time stamps in space-time such that we maximise the time step sizes used, and resolves the momentum exchange implicitly. It is combined with various acceleration techniques which exploit multiscale geometry representations and multiscale behaviour in time. The collision time stamp detection in space-time in combination with the implicit solve of the actual collision equations avoids that particles get locked into tiny time step sizes, the clustering yields a high concurrency level, and the acceleration techniques plus local time stepping avoid unnecessary computations. This brings a scaling, adaptive time stepping for DEM for real-world challenges into reach.

cs.MS↗

arXiv2023

GPU Offloading in ExaHyPE Through C++ Standard Algorithms

The ISO C++17 standard introduces \emph{parallel algorithms}, a parallel programming model promising portability across a wide variety of parallel hardware including multi-core CPUs, GPUs, and FPGAs. Since 2019, the NVIDIA HPC SDK compiler suite supports this programming model for multi-core CPUs and GPUs. ExaHyPE is a solver engine for hyperbolic partial differential equations for complex wave phenomena. It supports multiple numerical methods including Finite Volumes and ADER-DG, and employs adaptive mesh refinement with dynamic load balancing via space-filling curves as well as task-based parallelism and offloading to GPUs. This study ports ExaHyPE's tasks over blocks of Finite Volumes to the ISO C++ parallel algorithms programming model, and compares its performance and usability against an OpenMP implementation with offloading via OpenMP target directives. It shows that ISO C++ is a feasible programming model for non-trivial applications like our task-based AMR code. The realisation is bare of vendor-specific or non-C++ extensions. It however is slower than its OpenMP counterpart. \vspace{-1cm}

cs.MS↗

arXiv2022

A multiresolution Discrete Element Method for triangulated objects with implicit timestepping

Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are non-spherical. The most expensive part within such a simulation code is the collision detection. We propose a family of novel multiscale collision detection algorithms that can be applied to triangulated objects within explicit and implicit time stepping methods. They are well-suited to handle objects that cannot be represented by analytical shapes or assemblies of analytical objects. Inspired by multigrid methods and adaptive mesh refinement, we determine collision points iteratively over a resolution hierarchy, and combine a functional minimisation plus penalty parameters with the actual comparision-based geometric distance calculation. Coarse surrogate geometry representations identify "no collision" scenarios early on and otherwise yield an educated guess which triangle subsets of the next finer level potentially yield collisions. They prune the search tree, and furthermore feed conservative contact force estimates into the iterative solve behind an implicit time stepping. Implicit time stepping and non-analytical shapes often yield prohibitive high compute cost for rigid body simulations. Our approach reduces these cost algorithmically by one to two orders of magnitude. It also exhibits high vectorisation efficiency due to its iterative nature.

cs.CG↗

arXiv2022

Spherical accretion of collisional gas in modified gravity I: self-similar solutions and a new cosmological hydrodynamical code

The spherical collapse scenario has great importance in cosmology since it captures several crucial aspects of structure formation. The presence of self-similar solutions in the Einstein-de Sitter (EdS) model greatly simplifies its analysis, making it a powerful tool to gain valuable insights into the real and more complicated physical processes involved in galaxy formation. While there has been a large body of research to incorporate various additional physical processes into spherical collapse, the effect of modified gravity (MG) models, which are popular alternatives to the $ΛCDM$ paradigm to explain the cosmic acceleration, is still not well understood in this scenario. In this paper, we study the spherical accretion of collisional gas in a particular MG model, which is a rare case that also admits self-similar solutions. The model displays interesting behaviours caused by the enhanced gravity and a screening mechanism. Despite the strong effects of MG, we find that its self-similar solution agrees well with that of the EdS model. These results are used to assess a new cosmological hydrodynamical code for spherical collapse simulations introduced here, which is based on the hyperbolic partial differential equation engine ExaHyPE 2. Its good agreement with the theoretical predictions confirms the reliability of this code in modelling astrophysical processes in spherical collapse. We will use this code to study the evolution of gas in more realistic MG models in future work.

astro-ph.CO↗

arXiv2021

Doubt and Redundancy Kill Soft Errors -- Towards Detection and Correction of Silent Data Corruption in Task-based Numerical Software

Resilient algorithms in high-performance computing are subject to rigorous non-functional constraints. Resiliency must not increase the runtime, memory footprint or I/O demands too significantly. We propose a task-based soft error detection scheme that relies on error criteria per task outcome. They formalise how ``dubious'' an outcome is, i.e. how likely it contains an error. Our whole simulation is replicated once, forming two teams of MPI ranks that share their task results. Thus, ideally each team handles only around half of the workload. If a task yields large error criteria values, i.e.~is dubious, we compute the task redundantly and compare the outcomes. Whenever they disagree, the task result with a lower error likeliness is accepted. We obtain a self-healing, resilient algorithm which can compensate silent floating-point errors without a significant performance, I/O or memory footprint penalty. Case studies however suggest that a careful, domain-specific tailoring of the error criteria remains essential.

cs.SE↗

arXiv2021

Task inefficiency patterns for a wave equation solver

The orchestration of complex algorithms demands high levels of automation to use modern hardware efficiently. Task-based programming with OpenMP 5.0 is a prominent candidate to accomplish this goal. We study OpenMP 5.0's tasking in the context of a wave equation solver (ExaHyPE) using three different architectures and runtimes. We describe several task-scheduling flaws present in currently available runtimes, demonstrate how they impact performance and show how to work around them. Finally, we propose extensions to the OpenMP standard.

cs.DC↗