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DTSTAMP:20260625T133336Z
LOCATION:Bldg. 8 - Entrance Hall
DTSTART;TZID=Europe/Stockholm:20260630T173000
DTEND;TZID=Europe/Stockholm:20260630T194500
UID:submissions.pasc-conference.org_PASC26_sess135_posC102@linklings.com
SUMMARY:ACMP08 - Matrix-Free vs. Matrix-Based Finite Element Solvers for 3
 D Advection–Diffusion–Reaction Equations
DESCRIPTION:Zhaohui Song (Politecnico di Milano)\n\nHigh-order finite elem
 ent methods are attractive for three-dimensional advection–diffusion–react
 ion (ADR) problems, but their efficiency on distributed-memory systems is 
 often limited by memory traffic and communication in large linear solves. 
 This work compares matrix-based (MAT) and matrix-free (MF) finite element 
 solvers for a 3D ADR model on CPU-based HPC systems using deal.II. Both ap
 proaches use the same high-order Q3​ discretization, mesh partitioning, an
 d pure-MPI execution, allowing performance differences to be attributed so
 lely to operator realization. In the matrix-based approach, a global spars
 e matrix is assembled and applied via sparse matrix–vector products, while
  the matrix-free approach applies the operator on the fly using cell-wise 
 evaluations without forming the matrix. For symmetric diffusion–reaction p
 roblems solved with conjugate gradients, the matrix-free method achieves l
 ower time-to-solution due to reduced memory traffic. For nonsymmetric ADR 
 problems solved with restarted GMRES, global reductions limit strong scali
 ng for both approaches, but matrix-free operators remain more efficient. O
 n the largest steady test case with 5.9 million degrees of freedom, matrix
 -free methods reduce aggregate memory usage by up to 4.75×. A time-depende
 nt implicit Crank–Nicolson test further confirms that matrix-free methods 
 lower both memory consumption and per-iteration solve time when linear sys
 tems must be solved at every time step.\n\n
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