The stochastic Galerkin approach is a widely used method for quantifying uncertainty in dynamical systems. A polynomial chaos expansion of physical variables is used to represent uncertainty. Thus the evolution equations for the dynamics of ...

Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their ...

Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, which significantly relax restrictions on timestep ...

• Traditional splitting methods are cast as GARK methods.
• We show that all the ...

Splitting-based time integration approaches such as fractional step, alternating direction implicit, operator splitting, and locally one dimensional methods partition the system of interest into components, and solve individual ...

This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on a linear control variate framework. The approach allows for rigorous multifidelity extensions of the EnKF, where the uncertainty in coarser fidelities in the ...

This work develops novel time integration methods for the compressible Euler equations in the Lagrangian frame that are of arbitrary high order and exactly preserve the mass, momentum, and total energy of the system. The equations are considered in ...

Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations ...

Many scientific applications require the solution of large initial-value problems, such as those produced by the method of lines after semi-discretization in space of partial differential equations. The computational cost of implicit ...

Multirate time integration methods apply different step sizes to resolve different components of a system based on local activity levels. This local selection of step sizes allows increased computational efficiency while achieving the desired solution ...

This paper develops an efficient and parallel implementation of dynamically data-driven application systems inference using an ensemble Kalman filter based on shrinkage covariance matrix estimation. The proposed implementation works as follows: ...

The multivariate predictions of local reduced-order-models (MP-LROM) methodology, recently proposed by the authors Moosavi et al. (0000), uses machine learning based regression methods to predict the errors of reduced-order models. ...

Many scientific and engineering applications require the solution of large systems of initial value problems arising from method of lines discretization of partial differential equations. For systems with widely varying time scales, or with complex ...

Linearly implicit Runge-Kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part, e.g. reaction-diffusion systems. However, the use of approximate factorization ...

Implicit---explicit (IMEX) time stepping methods can efficiently solve differential equations with both stiff and nonstiff components. IMEX Runge---Kutta methods and IMEX linear multistep methods have been studied in the literature. In this paper we ...

The FATODE, which is extracted from the KPP numerical libraray, is a Fortran programming library for the integration of stiff ODE systems. It incorporates a set of generic linear solvers suitable for large sparse systems. And the set allows users to add ...

We investigate the behavior of adaptive time stepping numerical algorithms under the reverse mode of automatic differentiation (AD). By differentiating the time step controller and the error estimator of the original algorithm, reverse mode AD generates ...

In this paper we present the construction of a standardized adjoint of the global GEOS-Chem model. Adjoint models are powerful tools for estimating the sensitivity of (a function of) the model output with respect to a large number of inputs. The ...

This paper constructs multirate linear multistep time discretizations based on Adams-Bashforth methods. These methods are aimed at solving conservation laws and allow different timesteps to be used in different parts of the spatial domain. The proposed ...

Atmospheric chemical transport models (CTMs) are essential tools for the study of air pollution, for environmental policy decisions, for the interpretation of observational data, and for producing air quality forecasts. Many air quality studies require ...

This paper constructs multirate time discretizations for hyperbolic conservation laws that allow different timesteps to be used in different parts of the spatial domain. The proposed family of discretizations is second order accurate in time and has ...