The "Purdue Workshop on Grand Challenges in Computer Architecture for the Support of High Performance Computing" was sponsored by the National Science Foundation to identify critical research topics in computer architecture as they relate to high performance computing. Following a wide-ranging discussion of the computational characteristics and requirements of the grand challenge applications, the workshop identified four major computer architecture grand challenges as crucial to advancing the state of the art of high performance computation in the coming decade. These are: (1) idealized parallel computer models; (2) usable peta-ops (1015 ops) performance; (3) computers in an era of HDTV, gigabyte networks, and visualization; and (4) infrastructure for prototyping architectures. This report overviews some of the demands of the grand challenge applications and presents the above four grand challenges for computer architecture. © 1992.