We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

Modeling and simulation, particularly flow modeling using Computational Fluid Dynamics (CFD), is critical to the design of advanced jet engines. GE’s needs and advances in CFD mirror in many respects the NASA 2030 vision and GE is leveraging to good effect advances in high performance computing as the compute power pushes to Exascale.  A number of recent examples will be shared highlighting the ways GE is using advanced compute power and CFD.

The significant role of employing Computational Fluid Dynamics (CFD) for the development of field-deployable innovative remedies for oil, water, and gas separation and stabilization will be presented. Oil and gas wells are two typical types of wells known to produce hydrocarbons in varying rates and compositions. Oil wells produce a multiphase fluid, consisting of a mixture of oil, water and gas at different ratios. Gas wells produce gas at the core of the production tubular, and condensate with an annular flow regime on the inner wall of the production tubulars. In order to achieve a consistent supply of oil and gas production for the company, numerous technologies were developed in-house at the Aramco R&D Center, with emphasis on mitigating adverse conditions as they arise. A few examples will be presented during the talk, the focus will be on how CFD interventive remedies improved the performance and debottlenecking of Low Pressure Degassing Tanks (LPDT) in the company. The talk will also illustrate how CFD is used to create robust, reliable, and efficient remedies to boost operational performance for various purposes across the company’s operations.

High fidelity simulations of reacting flows involves a large number of solution variables and chemical reactions at vastly different spatial and time scales, making it one of the most extreme computational challenge. This work aims to achieve the goal of accelerated computing in twofold. First, the chemistry computations are performed on modern GPUs by replacing the conventional Arrhenius rate equations with the matrix-based formulation without introducing any approximations. Then the GPU-optimized linear algebra library, cuBLAS, is used to perform the matrix algebra and calculate the species source terms. In comparison to Cantera, the matrix-based approach results in up to three orders of magnitude faster source term computation and 3.5x reduced time-to-solution of high-fidelity direct numerical simulations (DNS) of reacting flows. Unlike the artificial/deep neural networks (rely on training data for predictions), the present matrix-based formulation solves the exact rate equations making it a general framework for any flow/flame configuration and fuel-air mixtures. Secondly, the complex mathematical systems are reduced by an automated mathematical framework based on computational singular perturbation and principal component analysis in order to reduce the dimensionality and dynamic range of the time scales. An artificial neural network algorithm is also employed as an efficient surrogates of the local projection basis. The feasibility of the approach is tested in canonical model problems of reacting systems.

We will discuss the current state of the art of very large multiphase flow simulations for flows involving very large ranges of scales, such as those involving liquid jet high speed atomisation producing very small droplets, the ladle flows in metallurgy at very large Schmidt numbers, and the boiling flows at large Jakob numbers. It is likely that high performance octree and VOF methods will not by sufficient to reach the exascale and that other techniques, such as time parallelisation, will be needed.

As we look toward future computing advances and how they will be used within the aerospace industry, it is valuable to identify multiple use cases to accelerate the combination of computing availability, tool readiness, and engineering process maturity. Aerospace CFD has had significant impact in many facets beyond use as a “computational wind tunnel” to predict aerodynamic forces but also leading to improved understanding of the entire vehicle. Present trends are demonstrating increases in capability through engineering application of large time-dependent simulations and initiatives moving toward model-based engineering. The past and future successes will require having the right tools and processes in place, along with the computational infrastructure. In this presentation, I will review present uses and trends in aerospace CFD with a projection toward potential use cases at exascale in order to identify paths forward for tools and processes to mature in tandem with computing capacity.

Upcoming exascale architectures require rethinking of the numerical algorithms used in large-scale PDE-based applications. These architectures favor algorithms, such as high-order finite elements, that expose fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. In this talk we present an overview of MFEM [1], a scalable library for high-order finite element discretization of PDEs on general unstructured grids. We also report on recent work in the Center for Efficient Exascale Discretizations [2], a co-design center in the US Exascale Computing Project focused on next-generation discretization software and algorithms. Our approach to efficient operator evaluation is based on a "matrix-free" representation of the finite element operator, that factors a bilinear form into a series of sparse and dense components corresponding to the parallelism, mesh topology, basis, geometry, and pointwise physics in the problem. The operator decomposition exposes several layers of parallelism, enables the use of batched dgemss and tensor contractions, and only requires quadrature point values to be assembled for computing the action. This "partial assembly" formulation is a natural fit for modern HPC hardware, because it results both in less (nearly optimal) computation and less (optimal) data movement compared to assembling a global sparse matrix, therefore increasing performance and reducing time to solution. In addition to discussing efficient operator evaluation, we will provide an overview of the MFEM capabilities and applications to compressible hydrodynamics and electromagnetics. We will also review our work on performance optimizations for GPU architectures, high-order benchmarks and miniapps, scalable unstructured adaptive mesh refinement, high-order mesh optimization and matrix-free preconditioning. [1] MFEM: Modular finite element library, http://mfem.org. [2] Center for Efficient Exascale Discretizations, http://ceed.exascaleproject.org.

Human-scale Mars vehicles will require retropropulsion for descent and landing, replacing heritage supersonic parachute systems with an extended phase of powered flight. Due to the limitations of terrestrial testing in Mars-relevant conditions, design and analysis will increasingly rely on computational modeling and simulation. This paper provides an overview of a computational campaign investigating the aerodynamics of a Mars lander concept along various points on a powered descent trajectory including supersonic, transonic, and subsonic conditions using finite-rate chemistry. Simulations using unstructured grids containing billions of elements are performed at scale using thousands of GPUs, enabling run-times of a few days for each simulation presented.

This presentation will introduce work in the U.S. Exascale Computing Project (ECP), which is developing a capable computing software ecosystem that leverages unprecedented HPC resources to work toward predictive science capabilities to solve problems in the areas of climate, energy, and human health. We will give an overview of the applications and software technologies being developed as part of the ECP, where software complexity is increasing due to disruptive changes in computer architectures and the complexities of tackling new frontiers in extreme-scale modeling, simulation, and analysis. We will give examples of the challenges application teams have faced in the development of new algorithms and physics capabilities that perform well on GPU accelerated node architectures. We will also describe our integrated approach to the deployment of a suite of programming models and runtimes, math libraries, data and visualization packaged and development tools that comprise the Extreme-scale Scientific Software Stack (E4S). We will explain how E4S—a portfolio-driven effort in ECP to collect, test, and deliver the latest advances in open-source HPC software technologies—is helping to overcome challenges associated with using independently developed software tools together in a single application. We conclude by showcasing some of the latest results the ECP teams have achieved in developing new capabilities in a number of application areas.

With the increasing prevalence of data from increasingly large full-fidelity flow simulations, there is a growing temptation to rely solely on these rich databases and exclusively data-based modeling paradigms, essentially abandoning physics-based modeling. However, the challenge with exclusively data-based modeling will always be model extrapolation: even with exascale computing and beyond, some regimes of relevant parameter spaces will never be computationally accessible with full-fidelity flow simulations. Additionally, physics-based models, being grounded in fundamental governing equations, need not re-learn fundamental constraints such as conservation laws and thermodynamics bounds. Unfortunately, especially for complex flows, such as turbulent multi-physics flows, every exclusively physics-based model will ultimately need to rely to some degree on crude assumptions or model oversimplification. Therefore, an opportunity exists to develop truly predictive models that can leverage the best of both physics-based modeling and data-based modeling through hybridization. The emerging paradigm starts with a physics-based modeling framework and replaces sub-model components with the crudest assumptions with data-based sub-model components derived from full-fidelity flow simulation databases. This hybridized modeling paradigm allows for not only more accurate models but also models able to account for phenomena that previous exclusively physics-based models were unable to capture. Several relevant examples from turbulent reacting flows will be presented and discussed.

Abstract

The recognition of the role hemodynamic forces have in the localization and developm

Traditional HPC simulations and AI / Big Data applications face similar challenges when solving extreme-scale scientific problems: bulk synchronous parallelism, expensive data motion, high algorithmic complexity and large memory footprint. Processors and memory technology scaling have mitigated these challenges thanks to an exponential growth in processor performance but only a constant increase in memory speed and capacity. The free lunch is perhaps over as we approach the hard physical limit of silicon. The energy efficiency gap between communication and computation keeps widening and has even forced the hardware and software communities for an immediate action of co-design. We describe the challenges encountered during the last 15-year journey of reshaping high performance linear algebra libraries for massively parallel systems. We explore disruptive numerical algorithms and programming models required to continue supporting HPC applications as well as emerging AI workloads at the dawn of the exascale age. In particular, we assess our implementation using 3D unstructured mesh deformation based on Radial Basis Function interpolation in the context of the HiCMA numerical library. Our HPC software solution achieves significant performance superiority against state-of-the-art implementations on Shaheen-II (based on dual-socket 16-core Intel Haswell nodes), Hawk (based on dual-socket 64-core AMD Epyc Rome nodes), and Fugaku (based on 48-core Fujitsu A64FX nodes) Supercomputers.

Exaflop Computing is driven by research activities with a focus on the performance but little regard for operational issues as are required by industrial users. In this talk we will address the industrial view of Exascale Computing aiming at getting a better understanding of what it takes to exploit teh new technologies also in the industrial field.

Abstract

We present an embedded approach for the numerical simulation of fluid-structure interacti

Together with the algorithm suitability to exploit current petascale and next-generation exascale supercomputers, robust, accurate, and structure-preserving discretizations are necessary for developing predictive computational tools. In this seminar, we will show how we leverage a multidisciplinary platform that integrates numerical analysis, physics, and high-performance computing for the analysis and development of novel numerical methods for ordinary and partial differential equations with provable properties such as nonlinear stability (entropy stability) and conservation, and structure-preserving techniques. These properties are critical for designing reliable, efficient, and self-adaptive solvers for complex geometries – an essential cornerstone for next-generation computational frameworks. Current classes of partial differential equations that we are working on are the compressible Navier–Stokes equations and the Eulerian model for compressible heat-conducting flows. We also use deep learning to complement and speed up the process of solving efficiently large-scale PDE-based problems. In this talk, we will summarize the progress we made in the last few years in the following areas: - Numerical analysis and algorithm development for robust, smart compressible flow solvers. - Development from the ground up of a new scalable hp-adaptive computational fluid dynamics (CFD) framework, a potential prototype of the future compressible solver as chartered by the NASA CFD 2030 vision. I will show applications and impact in the automotive and aerospace industry and in its extension for improving knowledge of flow physics in aeroacoustics.

The King Abdullah University of Science and Technology (KAUST), founded in 2009 in a 45-sq km academic village on the shores of the Red Sea, was created to be a 21st century “House of Wisdom” in the tradition of the 9th century Bayt al Hikmah that gave the world much of its modern mathematics, physics, chemistry, and medicine. KAUST is singular, or nearly so, among universities worldwide. The environment is one in which both long-term high-risk curiosity-driven research and goal-oriented research thrive. It is a post-graduate-only (primarily doctoral) institution, structured organizationally to lower barriers to interdisciplinary work. It offers awesome research facilities. It hosts on its own campus research labs of major multinational corporations and it incubates start-ups. Its residential community has a global composition of more than 120 countries with no majority or “group think.” It is hosted by a dynamically awakening country full of opportunities for creative young talents. Any one of these highly desirable features can make a university stand out. KAUST has them all! But to understand what KAUST offers to researchers, students, collaborators, and the world of stakeholders one should know a bit more. We summarize KAUST’s research paradigms and pillars, its strategies, and its mission. We also assess KAUST after its first 12 years of operations.

It is well known how humanity has contributed to technological progress based, long ago, on empirical results and currently seeking to use the advances that technology itself has to offer. This synergistic effect has accelerated in recent years and one of the factors that has led to this exponential growth is the advent of increasingly powerful computers that allow us to recreate the physical phenomena behind all innovation in virtual form. But it's not just about assigning the success of this synergy to the hardware. There is also a share of responsibility to the contribution that from the theory of computer science, from mathematics and from physics and chemistry has produced today the appearance of a discipline that we can summarize in computational mechanics. This ability to anticipate problems that may arise in the development of a product or process positions us more quickly and safely in an advantageous situation. It is not only anticipating, it is also better understanding what this kind of virtual radiography offers us when simulating a problem. In this work we intend to show some examples that, arising from industrial problems or from technology itself, allowed us to deepen with a scientific method in order to offer more and better solutions than those of good engineering practices developed long ago. In addition to being inside a land where a Technology Park operates (www.ptlc.org.ar), our Institute helps the growth of spin-offs, many of them inspired by lines of research supported by computational mechanics, which makes the minimum viable product more accessible for its delivery to the market.

In this work we describe a methodology to approximate the incompressible Navier-Stokes equations in time dependent domains. To deal with the motion of the domain, we employ a fixed-mesh method that we call fixed-mesh ALE. It consists of writing the equations in a moving ALE reference system but then projecting them onto a fixed background mesh. This implies that the boundaries of the elements do not necessarily coincide with the physical boundaries, and thus there is the possibility of badly cut elements. We use a Nitsche's type formulation to prescribe the boundary conditions and stabilise the bad cuts introducing a term that penalises the gradient of the unknown orthogonal to the finite element space in a patch that contains the badly cut element. The flow formulation is a stabilised finite element method that allows one to treat convection dominated flows and to use equal velocity pressure interpolation. Furthermore, this formulation can be shown to behave as an implicit large eddy simulation approach. A key issue is that the sub-grid scales on which the formulation depends are allowed to be time dependent; this fact has proved to be crucial for the robustness of the approach. Finally, the calculation of the velocity and the pressure is segregated by using a fractional step scheme designed at the pure algebraic level. The strategy described is applied to real life problems, and in particular to the simulation of the air flow generated by a train moving inside a tunnel.