Stabilized linear semi-implicit schemes for the nonlocal Cahn–Hilliard equation
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It is widely accepted that the next lepton collider beyond a Higgs factory would require center-of-mass energy of the order of up to 15 TeV. Since, given reasonable space and cost restrictions, conventional accelerator technology reaches its limits near this energy, high-gradient advanced acceleration concepts are attractive. Advanced and novel accelerators (ANAs) are leading candidates due to their ability to produce acceleration gradients on the order of 1–100 GV/m, leading to compact acceleration facilities. However, intermediate energy facilities (IEF) are required to test the critical technology elements on the way towards multi-TeV-class colliders. Here a science case for a 20–100 GeV center-of-mass energy ANA-based lepton collider that can be a candidate for an intermediate energy facility is presented. The IEF can provide numerous opportunities for high energy physics studies including precision Quantum Chromodynamics and Beyond the Standard Model physics measurements, investigation of charged particle interactions with extreme electromagnetic fields, and exploring muon and proton beam acceleration. Possible applications of this collider include the studies of γγ and electron beam-fixed target/beamdump collider designs. Thus, the goal of the proposed IEF is to both carry out particle physics measurements in the 20-100 GeV ranges as well as to serve as an ANA demonstrator facility.
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Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.