Related papers: Mixed-Precision in adaptive Runge-Kutta method for…
As CMOS scaling reaches its technological limits, a radical departure from traditional von Neumann systems, which involve separate processing and memory units, is needed in order to significantly extend the performance of today's computers.…
Mixed precision training (MPT) is becoming a practical technique to improve the speed and energy efficiency of training deep neural networks by leveraging the fast hardware support for IEEE half-precision floating point that is available in…
We present novel entropy-conservative and entropy-stable multirate Runge-Kutta methods based on Paired Explicit Runge-Kutta (P-ERK) schemes with relaxation for conservation laws and related systems of partial differential equations.…
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving $\min_{E,r}…
A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the…
In this paper, we propose two mixed precision algorithms for Block-Jacobi preconditioner(BJAC): a fixed low precision strategy and an adaptive precision strategy. We evaluate the performance improvement of the proposed mixed precision BJAC…
Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution…
This study computes the gradient of a function of numerical solutions of ordinary differential equations (ODEs) with respect to the initial condition. The adjoint method computes the gradient approximately by solving the corresponding…
Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…
In this paper, we develop a higher order symmetric partitioned Runge-Kutta method for a coupled system of differential equations on Lie groups. We start with a discussion on partitioned Runge-Kutta methods on Lie groups of arbitrary order.…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
A focus of recent research in quantum computing has been on developing quantum algorithms for differential equations solving using variational methods on near-term quantum devices. A promising approach involves variational algorithms, which…
The Met Office's weather and climate simulation code the Unified Model is used for both operational Numerical Weather Prediction and Climate modelling. The computational performance of the model running on parallel supercomputers is a key…
This paper investigates the performance of a subclass of exponential integrators, specifically explicit exponential Runge--Kutta methods. It is well known that third-order methods can suffer from order reduction when applied to linearized…
We use generalized Gaussian quadratures for exponentials to develop a new ODE solver. Nodes and weights of these quadratures are computed for a given bandlimit $c$ and user selected accuracy $\epsilon$, so that they integrate functions…
We propose an adaptive mixed precision and dynamically scaled preconditioned conjugate gradient algorithm (AMP-PCG). It dynamically adjusts the precision for storing vectors and computing, exploiting low precision when appropriate, while…
We consider quadrature formulas of high order in time based on Radau-type, L-stable implicit Runge-Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs…
GPU has a significantly higher performance in single-precision computing than that of double precision. Hence, it is important to take a maximal advantage of the single precision in the CG inverter, using the mixed precision method. We have…
We report on an analog computing system with coupled non-linear oscillators which is capable of solving complex combinatorial optimization problems using the weighted Ising model. The circuit is composed of a fully-connected 4-node LC…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…