Partial Flow Sensitivity

Compiler optimizations need precise and scalable analyses to discover program properties. We propose a partially flow-sensitive framework that tries to draw on the scalability of flow-insensitive algorithms while providing more precision at some specific program points. Provided with a set of critical nodes — basic blocks at which more precise information is desired — our partially flow-sensitive algorithm computes a reduced control-flow graph by collapsing some sets of non-critical nodes. The algorithm is more scalable than a fully flow-sensitive one as, assuming that the number of critical nodes is small, the reduced flow-graph is much smaller than the original flow-graph. At the same time, a much more precise information is obtained at certain program points than would had been obtained from a flow-insensitive algorithm.

KCL, Ray Theories and Application to Sonic Boom

We first review a general formulation of ray theory and write down the conservation forms of the equations of a weakly nonlinear ray theory (WNLRT) and a shock ray theory (SRT) for a weak shock in a polytropic gas. Then we present a formulation of the problem of sonic boom by a maneuvering aerofoil as a one parameter family of Cauchy problems. The system of equations in conservation form is hyperbolic for a range of values of the parameter and has elliptic nature else where, showing that unlike the leading shock, the trailing shock is always smooth.

Calculation of the front part of the sonic boom signature for a Maneuvering aerofopil

The sonic boom at a large distance from its source consists of a leading shock, a trailing shock and a one parameter family of nonlinear wavefronts in between these shocks. A new ray theoretical method using a shock ray theory and a weakly nonlinear lay theory has been used to obtain the shock fronts and wavefronts respectively, for a maneuvering aerofoil in a homogeneous medium. This method introduces a one parameter family of Cauchy problems to calculate the shock and wave fronts emerging from the surface of the aerofoil. These problems are solved numerically to obtain the leading shock front and the nonlinear wavefronts emerging from the front portion of the aerofoil.