WP1: Discretization

WP1 focuses on geometric domain representations (meshes), physics-based models, and space-time discretization methods optimized for exascale computing.

1. Recent Highlights (2024-2025)

CGAL 6.0 Release

Feature-preserving alpha wrapping integrated in CGAL 6.0

City-Scale Meshing

Ktirio-geom pipeline for city-scale watertight meshes

EuroHPC Benchmarks

Thermal-bridge and ParMMG benchmarks on EuroHPC systems

Multiphysics Ready

Domain-decomposition meshing for multiphysics applications

On the Road to Exascale

Thermomechanical simulations successfully scaled to over 4000 CPU cores

2. Objectives

The key objectives are twofold:

Geometric Domain Representations

Meshes are the main starting point for simulations. WP1 develops adaptive, multiresolution, robust-to-defects, and efficient parallel representations of large-scale models supporting:

  • Valid large-scale mesh generation from CAD or measurement data

  • Adaptive mesh refinement (AMR) for structured/unstructured grids

  • Nonconforming methods for parallel efficiency

  • All-hexahedral block grids for high-order methods

Physics-Based Models

Multiphysics coupling at multiple scales in space and time requires:

  • High-order methods to increase computational intensity and reduce communications

  • Nonconforming methods designed to avoid/reduce/minimize communications

  • Parallel-in-time strategies for evolution equations

  • Adaptive coupling techniques for multiphysics/multiscale problems

3. Workflow

Diagram

4. Key Tasks

T1.1: Mesh Generation

  • Valid large-scale mesh generation from defect-laden CAD/measurement data

  • Two-level mesh generation for nonconforming domain decomposition

  • All-hexahedral block structured meshes

T1.2-T1.3: Adaptive Mesh Refinement

  • Unstructured grids: Mmg/ParMmg scalability (billions of cells)

  • Cartesian/block grids: Patch-based, cell-based, wavelet multiresolution

  • Load-balancing algorithms for dynamic adaptation

T1.4: Finite Element Exascale Framework (FEEF)

  • High-order/spectral FEM on unstructured grids

  • Full de Rham complex support

  • Nonconforming methods with optimized kernels

T1.5: Nonconforming Methods

  • Trefftz, HDG, HHO, mortar element methods

  • Improved conditioning for iterative solvers

  • Integration with domain decomposition (WP3)

T1.6: Time-Strategy

  • Parallel-in-time (parareal) for parabolic PDEs and Hamiltonian systems

  • Error control for multiscale problems with relaxation sources

  • Adaptive operator splitting and multiresolution schemes

T1.7: Multiphysics Coupling

  • Partitioned discretization with field projections and conservations

  • Adaptive high-order coupling for heterogeneous physics

  • Multiscale coupling via discontinuous Galerkin and neural networks

5. Leads & Partners

Lead Institution

CEA

Co-Leaders

UNISTRA, INRIA, École Polytechnique, Sorbonne Université

Duration

Months 1-60

6. Addressed Exascale Bottlenecks

WP1 targets bottlenecks B2, B6, B7, B9, B10, B11-B13:

  • Communication reduction through high-order and nonconforming methods

  • Data movement efficiency via adaptive representations

  • Parallel scalability with AMR and domain decomposition

  • Resilience through robust mesh generation algorithms

7. Deliverables

ID Title Due Dates

D1.1-S

Software toolboxes for mesh generation/adaptation, space-time discretization and coupling

M24, M36, M48, M60

D1.2-MR

Activity reports (included in annual report D0.2-TR)

M12, M24, M36, M48, M60

D1.3-B

Benchmarking analysis report (bottlenecks and breakthroughs)

M12, M24, M36, M48, M60

8. Collaborations

  • ExaSoft: Low-level software infrastructure and performance portability

  • WP3: Solver integration for discretized systems

  • WP7: Benchmarking and CI/CD integration