Benson Muite

Kichakato Kizito

To determine the best method for solving a numerical problem modeled by a partial differential equation, one should consider the discretization of the problem, the computational hardware used and the implementation of the software solution. In solving a scientific computing problem, the level of accuracy can also be important, with some numerical m...

An overview of concerns observed in allowing for reproducibility in parallel applications that heavily depend on the three dimensional distributed memory fast Fourier transform are summarized. Suggestions for reproducibility categories for benchmark results are given.

The origin of stabilization of complex microstructures along macrotwin boundaries in martensites is explained by comparing two models based on Ginzburg-Landau theory. The first model incorporates a geometrically nonlinear strain tensor to ensure that the Landau energy is invariant under rigid body rotations, while the second model uses a linearized...

The cubic Klein-Gordon equation is a simple but non-trivial partial differential equation whose numerical solution has the main building blocks required for the solution of many other partial differential equations. In this study, the library 2DECOMP&FFT is used in a Fourier spectral scheme to solve the Klein-Gordon equation and strong scaling of t...

In this note, recently-derived high-order splitting schemes with complex coefficients for semilinear reaction-diffusion equations with periodic boundary conditions are shown to be most efficient when diffusion terms are much less stiff compared to reaction terms. An explanation for this is given in a simple setting.

A comparison of PGI OpenACC, FORTRAN CUDA, and Nvidia CUDA pseudospectral methods on a single GPU and GCC FORTRAN on single and multiple CPU cores is reported. The GPU implementations use CuFFT and the CPU implementations use FFTW. Porting pre-existing FORTRAN codes to utilize a GPUs is efficient and easy to implement with OpenACC and CUDA FORTRAN....

Nonlinear dispersive partial differential equations such as the nonlinear Schr\"odinger equations can have solutions that blow-up. We numerically study the long time behavior and potential blowup of solutions to the focusing Davey-Stewartson II equation by analyzing perturbations of the lump and the Ozawa exact solutions. It is shown in this way th...

The purpose of this paper is to present a comparison between the modified nonlinear Schr\"odinger (MNLS) equation and the focusing and defocusing variants of the (unmodified) nonlinear Schr\"odinger (NLS) equation in the semiclassical limit. We describe aspects of the limiting dynamics and discuss how the nature of the dynamics is evident theoretic...

We report on high resolution numerical studies of infinite Prandtl number convection using a simplified model with relevance to the motion of the Earth's mantle. Our model uses Navier-Stokes equations with the Boussinesq approximation and free slip velocity boundary conditions that is driven soley by internal heating. The 2D simulations are calcula...

The origin of stabilization of complex microstructures along macrotwin boundaries in martensites is explained by comparing two models based on Ginzburg-Landau theory. The first model incorporates a geometrically nonlinear strain tensor to ensure that the Landau energy is invariant under rigid body rotations, while the second model uses a linearized...

In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit-explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the...

Computations show that a two dimensional geometrically nonlinear Ginzburg-Landau model with inertia exhibits long lived metastable states, that have martensite domains with split tips and bent needles similar to those observed in NiAl. In comparison, the geometrically linear model quickly relaxes to states with twins which extend all the way across...

We solve a time dependent semilinear partial differential equation using a spectral collocation method on a distributed memory supercomputer. Previous attempts to use spectral methods to solve evolution- ary partial differential equations have scaled poorly on distributed memory machines because typical time stepping algorithms require fast global...

This work experimentally investigates the effects of an interstitial fluid on the discharge of granular material within an hourglass. The experiments include observations of the flow patterns, measurements of the discharge rates, and pressure variations for a range of different fluid viscosities, particle densities and diameters, and hourglass geom...

Regular perturbation solutions are obtained for the Stokes flow field, the first order effects of inertia on the flow field, and the primary and secondary pressure fields in the circular lid driven cavity. The physical mechanism that causes vortex breakdown exists at small Reynolds number; it is a stagnation of the secondary flow by an adverse pres...

Acceleration and sound measurements during granular discharge from silos are used to show that silo music is a sound resonance produced by silo quake. In tall and narrow silos, the latter is produced by stick–slip friction between the wall and the granular material. For the discharge rates studied, the occurrence of flow pulsations is determined pr...

Experimental measurements of discharge rate and observations of flow pattern were made for spherical, monosized particles in a liquid-filled, hourglass shaped container. Different combinations of fluid properties, solid properties and vessel geometry exhibited a range of flow patterns that are described as lubricated, fluidized, oscillatory, or loc...

A pseudo-spectral Fourier-Chebyshev collocation method for simulating a scalar two dimensional vis- coelastic dynamic model with capillarity is devel- oped. By using an integration matrix formulation for the Chebyshev modes, the numerical instabil- ity associated with large dimension Chebyshev dif- ferentiation matrices is overcome. The integration...