A5025339401- Numerical methods for differential equations
- Matrix Theory and Algorithms
- Advanced Numerical Methods in Computational Mathematics
- Electromagnetic Simulation and Numerical Methods
- Model Reduction and Neural Networks
- Fractional Differential Equations Solutions
- Computational Fluid Dynamics and Aerodynamics
- Radiative Heat Transfer Studies
- Differential Equations and Numerical Methods
- Modeling and Simulation Systems
- Advancements in PLL and VCO Technologies
- Advanced Photonic Communication Systems
- Meteorological Phenomena and Simulations
- Fluid Dynamics and Turbulent Flows
- Stability and Controllability of Differential Equations
- Semiconductor Lasers and Optical Devices
- Cardiomyopathy and Myosin Studies
- Gas Dynamics and Kinetic Theory
- Muscle Physiology and Disorders
- Cardiovascular Effects of Exercise
- Digital Filter Design and Implementation
- Iterative Methods for Nonlinear Equations
- Numerical methods in inverse problems
- Nuclear reactor physics and engineering
Tulane University
2023-2024
University of California, Merced
2020-2022
University of Washington
2020
University of Washington Applied Physics Laboratory
2017-2020
Proline substitutions within the coiled-coil rod region of β-myosin gene (MYH7) are predominant mutations causing Laing distal myopathy (MPD1), an autosomal dominant disorder characterized by progressive weakness distal/proximal muscles. We report that MDP1 mutation R1500P, studied in what we believe to be first mouse model for disease, adversely affected myosin motor activity despite being structural domain directs thick filament assembly. Contractility experiments carried out on isolated...
We introduce a new class of arbitrary-order exponential time differencing methods based on spectral deferred correction (ETDSDC) and describe simple procedure for initializing the requisite matrix functions. compare stability accuracy properties our ETDSDC meth- ods to those an existing implicit-explicit scheme (IMEXSDC). find that have larger regions comparable regions. conduct numerical experiments ETD IMEX schemes against competing fourth-order Runge-Kutta scheme. high-order are most...
We present a methodology for constructing time integrators solving systems of first-order ordinary differential equations by using interpolating polynomials. Our approach is to combine ideas from complex analysis and approximation theory construct new integrators. This strategy allows us trivially satisfy order conditions easily range implicit or explicit with properties such as parallelism high accuracy. In this work, we several example polynomial methods including generalizations the...
Abstract In this paper, we introduce a new framework for deriving partitioned implicit-exponential integrators stiff systems of ordinary differential equations and construct several time type. The approach is suited solving where the forcing term comprised additive nonlinear terms. We analyze stability, convergence, efficiency compare their performance with existing schemes such using numerical examples. also propose novel to visualizing linear stability schemes, which provides more...
Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 30 March 2020Accepted: 01 February 2021Published online: 13 May 2021Keywordstime-integration, polynomial interpolation, general linear methods, parallelism, high-order, exponential integratorsAMS Subject Headings65L04, 65L05, 65L06, 65L07Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industrial and Applied MathematicsCODEN: sjoce3
Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT coupled to other physics hydrodynamics, plasmas, etc., and the timescales one interested in capturing are often much slower than timescale. As result, treated implicitly, due its stiffness dimensionality, dominant computational cost multiphysics simulations. Here we develop new approach for implicit-explicit (IMEX)...
This work introduces a new class of Runge-Kutta methods for solving nonlinearly partitioned initial value problems. These methods, named (NPRK), generalize existing additive and component-partitioned allow one to distribute different types implicitness within nonlinear terms. The paper the NPRK framework discusses order conditions, linear stability, derivation implicit-explicit implicit-implicit integrators. concludes with numerical experiments that demonstrate utility viscous Burger's gray...
Recently a new class of nonlinearly partitioned Runge-Kutta (NPRK) methods was proposed for systems ordinary differential equations, $y' = F(y,y)$. The target problems are ones in which different scales, stiffnesses, or physics coupled nonlinear way, wherein the desired partition cannot be written classical additive component-wise fashion. Here we use rooted-tree analysis to derive full order conditions NPRK$_M$ methods, where $M$ denotes number partitions. Due coupling and thereby mixed...
Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT coupled to other physics hydrodynamics, plasmas, etc., and the timescales one interested in capturing are often much slower than timescale. As result, treated implicitly, due its stiffness dimensionality, dominant computational cost multiphysics simulations. Here we develop new approach for implicit-explicit (IMEX)...
Parareal is a well-known parallel-in-time algorithm that combines coarse and fine propagator within parallel iteration. It allows for large-scale parallelism leads to significantly reduced computational time compared serial time-stepping methods. However, like many methods it can fail converge when applied non-diffusive equations such as hyperbolic systems or dispersive nonlinear wave equations. This paper explores the use of exponential integrators Exponential are particularly interesting...
Abstract In this paper, we introduce a new framework for deriving partitioned implicit-exponential integrators stiff systems of ordinary differential equations and construct several time type. The approach is suited solving where the forcing term comprised additive nonlinear terms. We analyze accuracy stability compare their performance with existing schemes such using numerical examples. also propose novel to visualizing linear schemes, which provides more intuitive way understand...
In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The present is general and enables construction of many new families additive integrators with arbitrary order-of-accuracy varying degree implicitness. first work, focus on a class implicit-explicit block methods that are based fully implicit Runge–Kutta Radau nodes possess high stage order. We show (FIMEX) have improved stability compared existing IMEX methods, while also...
Polynomial multipoint methods are a new class of time-stepping schemes for solving first-order ordinary differential equations. The method construction is inspired by spatial spectral and allows arbitrarily high-orders accuracy as well parallelism across the method. Order, linear stability, adaptive implementation will be presented, similarities with existing general methods.