A fundamental trend of processor architecture evolving towards exaflops is fast increasing floating point performance (so-called "free" flops) accompanied by much slowly increasing memory and network bandwidth. In order to fully enjoy the "free" flops, a numerical algorithm of PDEs should request more flops per byte or increase arithmetic intensity. A meshfree/GFEM approximation can be the class of the algorithm. It is shown in a GFEM without extra dof that the kind of approximation takes advantages of the high performance of manycore GPUs by a high accuracy of approximation; the "expensive" method is found to be reversely hardware-efficient on the emerging architecture of manycore.