Famous Physicists and their Contributions to Physics | Philip Emeagwali

Back in the early 1980s, I was in College Park, Maryland. I was a research computational mathematician in College Park. The contributions to mathematics that I made in the early 1980s
were the cover stories of the top mathematics publications, such as the May 1990 issue
of the SIAM News that was published by the Society of Industrial and Applied Mathematics.
My quest for new mathematical knowledge was in the fields of calculus and numerical analysis.
My greatest focus was in the field of extreme-scaled computational mathematics.
I focused on never-before-seen ways
of using the most abstract
and the most advanced
arithmetical knowledge
and using that knowledge
to solve the toughest problems
that arise in computational physics
that otherwise will be unsolveable.
My new field
—of never-before-seen
extreme-scaled computations—
was at the crossroad
between calculus and algebra
and between arithmetic
and the computer.
I redefined my numerical analysis
as between
the singular processor
that computes sequentially
and my ensemble of processors
that computes in parallel,
or that solves many problems
at once.
In 1989, it made the news headlines
that an African supercomputer wizard
in the United States
had invented
how to use 65,536 processors
to solve as many problems in parallel.
I am that African supercomputer scientist
that was in the news
onward of 1989.
I was in the news because I invented
how to use one billion processors
to solve one billion
initial-boundary value problems
of calculus
and how to solve them in parallel
and, specifically, how to compute across
a new internet
that is a new global network of
two-raised-to-power sixteen
commodity-off-the-shelf processors
that were married together
as one seamless, cohesive
massively parallel processing supercomputer
and married together
by sixteen times as many
email wires.
The mathematical analysis
that was at the theoretical foundation
of my extreme-scale
computational mathematics
and that preceded
my invention
of the massively parallel processing supercomputer
is called
the stability analysis
of finite difference discretizations
of partial differential equations
of modern calculus.
Stability analysis
was the extremely rigorous
and the analytical procedure
that I used to derive a priori error estimate
of the rate of propagation
of initial errors
and the rate as I computed forward in time
and computed within each processor
and communicated across
my new ensemble of 65,536
tightly-coupled, commodity processors
with each processor
operating its own operating system
and with each processor
having its own dedicated memory
that shared nothing with each other.
After going through some dense
and abstract stability analyses
in the early 1980s
and after conducting companion computational experiments,
I mathematically discovered
that explicit finite difference
algebraic approximations
of the governing system of
partial differential equations
of modern calculus
that include the thirty-six (36)
new partial derivative terms
that I invented
allow longer computational time-steps
which, in turn, makes my calculations faster.
That mathematical invention
was how I greatly reduced
the vexing time-step limit
that textbooks on computational physics
describe as the Courant Condition.
That Courant Condition
is the necessary condition
for the convergence
of the numerical solution
of an explicit
partial difference equation
to the analytical solution
of the original partial differential equation
that it was approximating.
That mathematical invention
was how I bypassed
the empirical Darcy’s formula
that was outdated and invented
back in 1856.
That mathematical invention
was how I replaced
a system of nine algebraic Darcy’s equations
that must be used by the petroleum industry to describe
the subterranean motions
of multi-phased fluids.
I invented and replaced
those nine algebraic Darcy’s equations
with my more rigorous
system of nine partial differential equations
of a new calculus
that I invented
from first principles,
or from the Second Law of Motion
of physics.
Henry Darcy’s Law
is a statement in the fluid dynamics
of flows across a porous medium.
Henry Darcy’s Law
states that the velocities of crude oil, injected water,
and natural gas flowing across
the permeable Niger Delta oilfields
of southeastern Nigeria
is due to the difference in pressure.

TAGS: supercomputer, world’s fastest supercomputer, parallel processing, high performance computing, parallel computing, Grand Challenge Problems, vector processors, vector supercomputers, computational mathematics, computational physics, partial differential equations, algebra, calculus, black physicists, African American physicists, African American Inventors, black inventors, black history month, black scientist, famous black inventors

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