sphinx/source/intro.md

3 Historically, conventional high-order finite element methods were rarely used for industrial proble…
4 … point operations (FLOPS) per degree of freedom (DOF)---see {numref}`fig-assembledVsmatrix-free`--…
5 Nowadays, high-order numerical methods, such as the spectral element method (SEM)---a special case …
6 …---are employed, especially with (nearly) affine elements, because linear constant coefficient pro…
7 …-assembledVsmatrix-free` we analyze and compare the theoretical costs, of different configurations…
9 A more relevant performance plot for current state-of-the-art high-performance machines (for which …
10 …-order methods, implemented properly with only partial assembly, require optimal amount of memory …
11 Thus, high-order methods in matrix-free representation not only possess favorable properties, such …
13 (fig-assembledvsmatrix-free)=
16 …resentations of a linear operator for a PDE in 3D with $b$ components and variable coefficients ar…
17 … on the fly and stores a compact representation of the linearization at quadrature points. The rep…
18 The *assembled* representation uses a (block) CSR format.
21 …-performance implementations have often been special-purpose and intrusive. libCEED {cite}`libceed…
23 While libCEED's focus is on high-order finite elements, the approach is algebraic and thus applicab…
24 …a lightweight portable library that allows a wide variety of applications to share highly optimize…
25 …a low-level Application Programming Interface (API) for user codes so that applications with their…
27 libCEED provides a unified interface, so that users only need to write a single source code and can…
29 (fig-libceed-backends)=
32 The role of libCEED as a lightweight, portable library which provides a low-level API for efficient…