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1 ---
2 title: 'libCEED: Fast algebra for high-order element-based discretizations'
4 - high-performance computing
5 - high-order methods
6 - finite elements
7 - spectral elements
8 - matrix-free
10 - name: Jed Brown
11 orcid: 0000-0002-9945-0639
13 - name: Ahmad Abdelfattah
14 orcid: 0000-0001-5054-4784
16 - name: Valeria Barra
17 orcid: 0000-0003-1129-2056
19 - name: Natalie Beams
20 orcid: 0000-0001-6060-4082
22 - name: Jean-Sylvain Camier
23 orcid: 0000-0003-2421-1999
25 - name: Veselin Dobrev
26 orcid: 0000-0003-1793-5622
28 - name: Yohann Dudouit
29 orcid: 0000-0001-5831-561X
31 - name: Leila Ghaffari
32 orcid: 0000-0002-0965-214X
34 - name: Tzanio Kolev
35 orcid: 0000-0002-2810-3090
37 - name: David Medina
39 - name: Will Pazner
40 orcid: 0000-0003-4885-2934
42 - name: Thilina Ratnayaka
43 orcid: 0000-0001-6102-6560
45 - name: Jeremy Thompson
46 orcid: 0000-0003-2980-0899
48 - name: Stan Tomov
49 orcid: 0000-0002-5937-7959
52 - name: University of Colorado at Boulder
54 - name: Lawrence Livermore National Laboratory
56 - name: University of Tennessee
58 - name: Occalytics LLC
60 - name: University of Illinois at Urbana-Champaign
64 ---
73 Unfortunately, high-quality implementations have been relegated to applications and intrusive frame…
75 …d-user-manual], is a lightweight library that provides a purely algebraic interface for linear and…
76 … portable performance via run-time selection of implementations optimized for CPUs and GPUs, inclu…
77 …fers interfaces in C99 [@C99-lang], Fortran77 [@Fortran77-lang], Python [@Python-lang], Julia [@Ju…
78 …bCEED` at a low level into existing applications in place of existing matrix-vector products witho…
79 Alternatively, users can utilize integrated `libCEED` support in MFEM [@MFEMlibrary; @mfem-paper].
81 … for performance engineering and co-design, as well as an algebraic interface for solvers research…
95 …-block diagonal $D$ and stacking the restrictions $\mathcal E_e$ and basis actions $B_e$ for each …
99 …ement-based discretizations, with optimized implementations of the action and preconditioning ingr…
101 `libCEED`'s native C interface is object-oriented, providing data types for each logical object in …
104 ------ ------------ -----------
105 $D$ `CeedQFunction` User-defined action at quadrature points
108 $A$ `CeedOperator` Linear or nonlinear operator acting on L-vectors
111 …ecomposition}, and acts on a `CeedVector`, which typically encapsulates zero-copy access to host o…
112 …$\mathcal E$ requires mesh topology and a numbering of DoFs, and may be a no-op when data is alrea…
114 Some constructors are provided for arbitrary polynomial degree $H^1$ Lagrange bases with a tensor-p…
119 …-refinement and adaptivity (where $h$ commonly denotes the average element size and $p$ the polyno…
120 …s (transparently using the @NVRTCwebsite, HIPRTC, or OCCA [@OCCAwebsite] run-time compilation feat…
122 …e matrices (e.g., for coarse operators in multigrid) and construction of $p$-multigrid prolongatio…
123 Preconditioning matrix-free operators is an active area of research; support for domain decompositi…
126 elements with different topology. This sketch shows the independence of Q-functions
129 # High-level languages
131 `libCEED` provides high-level interfaces in Python, Julia, and Rust, each of which is maintained an…
133 …-cffi]. CFFI allows reuse of most C declarations and requires only a minimal adaptation of some of…
135 …-level interface, which is generated automatically from `libCEED`'s C header files, and a high-lev…
137 …-generated bindings from the `libCEED` C header files, offering increased safety due to Rust owner…
144 ![`libCEED` provides the algebraic core for element-based discretizations, with specialized impleme…
149 …-design Center for Efficient Exascale Discretization [@CEEDwebsite] has defined a suite of Benchma…
151 …-socket AMD EPYC 7452 (32-core, 2.35GHz) and the \texttt{cuda/gen} backend on LLNL's Lassen system…
155 …use for solver composition and leverage `libCEED`'s full capability for real-world applications, `…
156 The fluid dynamics example solves the 2D and 3D compressible Navier-Stokes equations using SU/SUPG …
157 …-Krylov solvers with $p$-multigrid preconditioners; \autoref{fig:Solids} shows a twisted Neo-Hooke…
161  without writing any `libCEED` Q-functions.
170 This research is supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort …