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MIXED FINITE ELEMENT METHOD FOR ELECTROWETTING ON DIELECTRIC WITH CONTACT LINE PINNING
FINITE ELEMENT CONTACT LINE PINNING
2015/12/11
We present a mixed finite element method for a model of the flow in
a Hele-Shaw cell of 2-D fluid droplets surrounded by air driven by surface tension
and actuated by an electric &...
The Embedded Boundary Integral Method (EBI) for the Incompressible Navier-Stokes equations
Embedded Boundary Integral Method (EBI) Incompressible Navier Stokes equations
2015/7/15
We present a new method for the solution of the unsteady incompressible Navier-Stokes equations. Our goal is to achieve a robust and scalable methodology for two and three dimensional incompressible f...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method
2015/7/8
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
Basket Options Valuation for a Local Volatility Jump-Diffusion Model with the Asymptotic Expansion Method
Basket options pricing local volatility jump-diffusionmodel forward PIDE asymp-totic expansion
2010/4/27
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We deri...
Convergence Analysis of the Adaptive Finite Element Method with the Red-Green Refinement
Adaptive Finite Element Method Convergence Analysis Red-Green Refinement
2015/5/6
Abstract. In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Ga...
APPLICATION OF ADOMIAN DECOMPOSITION METHOD TO SOLVING THE DUFFING-VAN DER POL EQUATION
Duffing-van der Pol equation Adomian decomposition method regular perturbation method
2008/11/26
In this paper, the Adomian decomposition method and the regular perturbation
method are used to study the Duffing-van der Pol equation. The two series solutions
obtained by each method are compared.
Derivation of Separable Amplitude Equations by Multiple Scales Method
Multiple Scales Method Three Component 2D Nonlinear Klein-Gordon Equation Separable Amplitude NLS Equation Spectral Problem Separable Integrable Hamiltonian system
2010/3/4
The method of multiple scales is used to derive separable nonlinear Schrödinger equations as amplitude equation from three component 2D nonlinear Klein-Gordon Equation. We further discuss the int...