Numerical Methods and Computers

Concepts for numerical optical computers

1. Background 2. Residue number system 2.1. Encoding 2.2. Decoding 2.3. Scaling 3. Basis for numerical methods 4. Processor design concepts 4.1. Cyclic phase implementation 4.2. Mapping with beam position control 4.3. Multipurpose arithmetic module 5. Extended computing applications 5.1. Polynomial evaluation 5.2. Matrix multiplication and transforms 6. Concluding remarks 7. References Abstract...

DIMSEMs - diagonally implicit single-eigenvalue methods for the numerical solution of stiff ODEs on parallel computers

This paper derives a new class of general linear methods (GLMs) intended for the solution of stiff ordinary differential equations (ODEs) on parallel computers. Although GLMs were introduced by Butcher in the 1960s, the task of deriving formulas from the class with properties suitable for specific applications is far from complete. This paper is a contribution to that work. Our new methods have...

Numerical Methods and Stochastics Part I: Numerical Methods

Numerical Study of Geometric Multigrid Methods on CPU--GPU Heterogeneous Computers

The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from many types of partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously. Graphics processing units (GPUs) have recently burst onto the scientific computing scene as a technology...

Viscosity and numerical methods

In any flow, layers move at different velocities and a fluid’s viscosity arises from the shear stress between the layers that ultimately oppose any applied force. These shear stresses are communicated via collisions between the particles comprising the fluid, and the typical scale of viscosity is therefore of order the mean free collisional length λ. This scale is usually much smaller than the ...