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We prove that the entropy solution to a scalar conservation law posed on the real line with a flux that is discontinuous at one point (in the space variable) coincides with the derivative of the solution to a Hamilton-Jacobi (HJ) equation…
We propose a CPU-GPU heterogeneous computing method for solving time-evolution partial differential equation problems many times with guaranteed accuracy, in short time-to-solution and low energy-to-solution. On a single-GH200 node, the…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
Multicore parallel programming has some very difficult problems such as deadlocks during synchronizations and race conditions brought by concurrency. Added to the difficulty is the lack of a simple, well-accepted computing model for…
Nowadays, we are to find out solutions to huge computing problems very rapidly. It brings the idea of parallel computing in which several machines or processors work cooperatively for computational tasks. In the past decades, there are a…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
Every Model of High-Level Computation (MHC) has an underlying composition mechanism for combining simple computing devices into more complex ones. Composition can be done by (explicitly or implicitly) defining control flow, data flow or any…
In this paper, we present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton's principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an…
Current supercomputers often have a heterogeneous architecture using both CPUs and GPUs. At the same time, numerical simulation tasks frequently involve multiphysics scenarios whose components run on different hardware due to multiple…
Networks of interconnected resistors, springs and beams, or pores are standard models of studying scalar and vector transport processes in heterogeneous materials and media, such as fluid flow in porous media, and conduction, deformations,…
The applications and impact of high fidelity simulation of fluid flows are far-reaching. They include settling some long-standing and fundamental questions in turbulence. However, the computational resources required for such efforts are…
Heterogeneity is omnipresent in today's commodity computational systems, which comprise at least one multi-core Central Processing Unit (CPU) and one Graphics Processing Unit (GPU). Nonetheless, all this computing power is not being…
We propose a parametric hyperbolic conservation law (SymCLaw) for learning hyperbolic systems directly from data while ensuring conservation, entropy stability, and hyperbolicity by design. Unlike existing approaches that typically enforce…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
This paper consists of three parts. The first part provides a unified programming model for heterogeneous computing with CPU and accelerator (like GPU, FPGA, Google TPU, Atos QPU, and more) technologies. To some extent, this new programming…
This article studies a hyperbolic conservation law that models a highly re-entrant manufacturing system as encountered in semi-conductor production. Characteristic features are the nonlocal character of the velocity and that the influx and…
We present a dataflow model for modelling parallel Unix shell pipelines. To accurately capture the semantics of complex Unix pipelines, the dataflow model is order-aware, i.e., the order in which a node in the dataflow graph consumes inputs…
The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…
Globular CW-complexes and flows are both geometric models of concurrent processes which allow to model in a precise way the notion of dihomotopy. Dihomotopy is an equivalence relation which preserves computer-scientific properties like the…
Computational fluid dynamics is a direct modeling of physical laws in a discretized space. The basic physical laws include the mass, momentum and energy conservations, physically consistent transport process, and similar domain of…