Short alpha-helix peptides or protein fragments are a common motif in biological membranes. These fragments can serve as anchors that tether functional groups of proteins at membrane surfaces. They can also organize into assemblies that may result in membrane spanning pores. Many antimicrobial peptides are thought to kill bacteria through interaction with the cell membrane alone, and one likely mechanism is the formation of nonspecific membrane spanning pores. From a computational perspective, studying these systems is quite complex. While one would like to apply an atomically rigorous simulation method, current algorithms and computer resources will allow for only a few simulations for a few nanoseconds. We have used a molecular theory based approach coupled with coarse-grained molecular models to attack this problem. More specifically we simultaneously compute the structure of a zero tension bilayer, the perturbations in that structure due to embedded peptides, and in the case of membrane spanning pores, the structure of the solvent in the pore. Note that all species (solvent, lipid head groups, lipid tail groups, and peptides) are treated on an equal footing in this approach. The numerical requirements of these calculations were significant. These molecular theories (often integral equations of finite range) are quite different than partial differential equations. Therefore, novel applied mathematics approaches are needed for efficient solution in two and three dimensions. Our algorithms combine parallel computing (100 distributed memory processors for this problem) with a Schur complement based solver approach. We make extensive use of arc-length continuation algorithms in order to study these membrane bound peptide assemblies. The calculations clearly show that barrel-stave pores are expected for very small assemblies. Toroidal pores, where the lipid head group-solvent interface bends through the pore, are preferred for larger pores. Finally we find a first order phase transition between unbound assemblies and assemblies that exhibit membrane spanning pores. In order to elucidate this phase behavior literally hundreds of calculations were required. This number of calculations for a three-dimensional system was greatly facilitated by optimization of solver algorithms specifically for these molecular theories. We expect that with further algorithms research, the resolution of the models will be improved, and the application space (e.g. larger proteins and protein assemblies) will be greatly expanded.