# Computing Spacetime Curvature via Differential-Algebraic Equations

## (Steven Lee, Oak Ridge National Laboratory)

*(Note: This talk will be held at 3:00 pm in Room 1-390!)*
The equations that govern the behavior of physical systems can often
be numerically solved using finite-difference (or finite-element)
discretizations and differential-algebraic equation (DAE) solvers.
For example, such an approach can be used to solve the Einstein field
equations of general relativity, and thereby simulate significant
astrophysical events. Fluid flow, heat transfer and other problems
can also be formulated and numerically solved as DAEs. In each case,
the differential equations describe the flow or motion of the physical
system, and the algebraic equations describe various conservation
laws, boundary conditions or constraints.

Fortunately, high-quality mathematical software for solving DAEs
exists (e.g., DASSL) and it can be used to solve a wide array of
difficult problems. This talk describes how DAE codes such as DASSL
can be enhanced in a way that enables scientists to efficiently solve
a larger range of important, multidimensional initial-value problems.
In particular, we describe some preliminary work in which the
gravitational field of a black hole is computed by solving some
simplified versions of the Einstein field equations.