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The advent of massively parallel supercomputers, with theirdistributed-memory technology using many processing units, has favored thedevelopment of highly-scalable local low-order solvers at the expense ofharder-to-scale global very high-order spectral methods. Indeed, FFT-basedmethods, which were very popular on shared memory computers, have been largelyreplaced by finite-difference (FD) methods for the solution of many problems,including plasmas simulations with electromagnetic Particle-In-Cell methods.For some problems, such as the modeling of so-called "plasma mirrors" for thegeneration of high-energy particles and ultra-short radiations, we have shownthat the inaccuracies of standard FD-based PIC methods prevent the modeling onpresent supercomputers at sufficient accuracy. We demonstrate here that a newmethod, based on the use of local FFTs, enables ultrahigh-order accuracy withunprecedented scalability, and thus for the first time the accurate modeling ofplasma mirrors in 3D.

Ultrahigh-order Maxwell solver with extreme scalability for electromagnetic PIC simulations of plasmas