An accuracy assessment of Cartesian-mesh approaches for the Euler equations
Journal of Computational Physics
A projection method for locally refined grids
Journal of Computational Physics
Stochastic partial differential equations: a modeling, white noise functional approach
Stochastic partial differential equations: a modeling, white noise functional approach
Applied numerical linear algebra
Applied numerical linear algebra
Mathematical physiology
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
Understanding Molecular Simulation
Understanding Molecular Simulation
Developments in Cartesian cut cell methods
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Incorporating Diffusion in Complex Geometries into Stochastic Chemical Kinetics Simulations
SIAM Journal on Scientific Computing
Simulating the blood-muscle-valve mechanics of the heart by an adaptive and parallel version of the immersed boundary method
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
Journal of Computational Physics
Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations
Journal of Computational Physics
Hi-index | 31.45 |
Stochastic partial differential equations are introduced for the continuum concentration fields of reaction-diffusion systems. The stochastic partial differential equations account for fluctuations arising from the finite number of molecules which diffusively migrate and react. Spatially adaptive stochastic numerical methods are developed for approximation of the stochastic partial differential equations. The methods allow for adaptive meshes with multiple levels of resolution, Neumann and Dirichlet boundary conditions, and domains having geometries with curved boundaries. A key issue addressed by the methods is the formulation of consistent discretizations for the stochastic driving fields at coarse-refined interfaces of the mesh and at boundaries. Methods are also introduced for the efficient generation of the required stochastic driving fields on such meshes. As a demonstration of the methods, investigations are made of the role of fluctuations in a biological model for microorganism direction sensing based on concentration gradients. Also investigated, a mechanism for spatial pattern formation induced by fluctuations. The discretization approaches introduced for SPDEs have the potential to be widely applicable in the development of numerical methods for the study of spatially extended stochastic systems.