An energy-stable convex splitting for the phase-field crystal equation
MetadataShow full item record
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method.
Showing items related by title, author, creator and subject.
Validation of two Framingham cardiovascular risk prediction algorithms in an Australian population: The 'old' versus the 'new' Framingham equationZomer, E.; Owen, A.; Magliano, D.; Liew, D.; Reid, Christopher (2011)Background: Multivariable risk prediction equations attempt to quantify an individual's cardiovascular risk. Those borne from the Framingham Heart Study remain the most well-established and widely used. In February 2008, ...
Comparison of predictive performance of renal function estimation equations for all-cause and cardiovascular mortality in an elderly hypertensive populationChowdhury, E.; Langham, R.; Owen, A.; Krum, H.; Wing, L.; Nelson, M.; Reid, Christopher; Second Australian National Blood Pressure Study Management Committeem (2015)BACKGROUND: The Modifications of Diet in Renal Disease (MDRD) and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) are 2 equations commonly used to estimate glomerular filtration rate (eGFR). The predictive ...
Numerical Solution of Second-Order Linear Fredholm Integro-Differential Equation Using Generalized Minimal Residual MethodAruchunan, Elayaraja; Sulaiman, J. (2010)This research purposely brought up to solve complicated equations such as partial differential equations, integral equations, Integro-Differential Equations (IDE), stochastic equations and others. Many physical phenomena ...