Ab initio molecular dynamics: Theory and Implementation

MODULE Densityrho(1:N x ,1:N y ,1:N z ) = 0FOR i=1:N b ,2scr(1:N x ,1:N y ,1:N z ) = 0FOR j=1:N PWscr(ipg(1,i),ipg(2,i),ipg(3,i)) = c(j,i) + I * c(j,i+1)scr(img(1,i),img(2,i),img(3,i)) = CONJG[c(j,i) + I * c(j,i+1)]ENDCALL FFT3D("INV",scr)rho(1:N x ,1:N y ,1:N z ) = rho(1:N x ,1:N y ,1:N z ) + && REAL[scr(1:N x ,1:N y ,1:N z )]**2 + IMAG[scr(1:N x ,1:N y ,1:N z )]**2ENDMODULE VPSIFOR i=1:N b ,2scr(1:N x ,1:N y ,1:N z ) = 0FOR j=1:N PWscr(ipg(1,i),ipg(2,i),ipg(3,i)) = c(j,i) + I * c(j,i+1)scr(img(1,i),img(2,i),img(3,i)) = CONJG[c(j,i) + I * c(j,i+1)]ENDCALL FFT3D("INV",scr)scr(1:N x ,1:N y ,1:N z ) = scr(1:N x ,1:N y ,1:N z ) * && vpot(1:N x ,1:N y ,1:N z )CALL FFT3D("FW",scr)FOR j=1:N PWFP = scr(ipg(1,i),ipg(2,i),ipg(3,i)) && + scr(img(1,i),img(2,i),img(3,i))FM = scr(ipg(1,i),ipg(2,i),ipg(3,i)) && - scr(img(1,i),img(2,i),img(3,i))fc(j,i) = f(i) * CMPLX[REAL[FP],IMAG[FM]]fc(j,i+1) = f(i+1) * CMPLX[IMAG[FP],-REAL[FM]]ENDEND3.9 Parallel Computing3.9.1 IntroductionAb initio molecular dynamics calculation need large computer resources. Memoryand cpu time requirement make it necessary to run projects on the biggest computersavailable. It is exclusively parallel computers that provide these resourcestoday. There are many different types of parallel computers available. Computersdiffer in their memory access system and their communication system. Widelydifferent performances are seen for bandwidth and latency. In addition, differentprogramming paradigms are supported. In order to have a portable code that canbe used on most of the current computer architectures, CPMD was programmed us-82