meson-mfem/src/include/serif/discretization/domain/schema/validation/boundary.hpp

#pragma once

#include <optional>
#include <tuple>
#include <vector>

#include "serif/discretization/domain/concepts.hpp"
#include "serif/discretization/domain/mesh/topology.hpp"
#include "serif/discretization/domain/relation/relations.hpp"
#include "serif/discretization/domain/relation/validation/runtime.hpp"
#include "serif/discretization/domain/schema/concepts.hpp"
#include "serif/discretization/domain/schema/validation/validator.hpp"

namespace serif::discretization::domain::schema::validation {
    using relation::DomainBoundary;

    using relation::validation::RelationValidationResult;
    using relation::validation::RelationValidationFailure;

    template <IsBoundary BoundaryT, IsDomainOrSet... DomainTs>
    struct RelationValidator<DomainBoundary<BoundaryT, DomainTs...>> {
        template <IsSchema SchemaT>
        [[nodiscard]] static RelationValidationResult validate(const mesh::MeshTopology &topology) {
            static_assert(
                sizeof...(DomainTs) == 1 || sizeof...(DomainTs) == 2,
                "DomainBoundary requires exactly one or two domains."
            );

            static_assert(
                SchemaT::template contains_boundary<BoundaryT>(),
                "DomainBoundary refers to a boundary which is not registered in the supplied DomainSchema."
            );

            static_assert(
                (SchemaT::template contains_domain<DomainTs>() && ...),
                "DomainBoundary refers to a domain which is not completely registered in the supplied DomainSchema."
            );

            constexpr int expectedBoundaryID = SchemaT::template boundary_id<BoundaryT>();

            using DomainsTuple = std::tuple<DomainTs...>;

            const auto make_diagnostics = [&](const int faceID, const int boundaryElementID, const std::optional<int> actualBoundaryID) {
                RelationValidationResult::DomainBoundaryDiagnostics diagnostics{
                    .faceID             = faceID,
                    .boundaryElementID  = boundaryElementID,
                    .expectedBoundaryID = expectedBoundaryID,
                    .actualBoundaryID   = actualBoundaryID
                };

                if (faceID < 0 || faceID >= topology.face_count()) {
                    return diagnostics;
                }

                const mesh::FaceElements faceElements = topology.face_elements(faceID);

                diagnostics.firstElementID  = faceElements.firstElementID;
                diagnostics.secondElementID = faceElements.secondElementID;

                if (diagnostics.firstElementID >= 0) {
                    diagnostics.firstDomainID = topology.element_domain_id(diagnostics.firstElementID);
                }
                if (diagnostics.secondElementID >= 0) {
                    diagnostics.secondDomainID = topology.element_domain_id(diagnostics.secondElementID);
                }

                return diagnostics;
            };

            // Check only the cardinality/topological shape required by the relation.
            //
            // One-domain form:
            //
            //     Domain | computational exterior
            //
            // Exactly one adjacent volume element must exist.
            //
            // Two-domain form:
            //
            //     DomainA | DomainB
            //
            // Both adjacent volume elements must exist.
            const auto has_required_topology = [](const int firstElementID, const int secondElementID) noexcept {
                if constexpr (sizeof...(DomainTs) == 1) {
                    const bool firstExists  = firstElementID >= 0;
                    const bool secondExists = secondElementID >= 0;

                    return firstExists != secondExists;
                } else {
                    return firstElementID >= 0 && secondElementID >= 0;
                }
            };

            // Determine whether a face is exactly one of the faces described by
            // DomainBoundary<BoundaryT, DomainTs...>. For two domains, ordering
            // is intentionally irrelevant.
            const auto face_matches_domains = [&topology](const int firstElementID, const int secondElementID) noexcept {
                if constexpr (sizeof...(DomainTs) == 1) {
                    using DomainT = std::tuple_element_t<0, DomainsTuple>;

                    const bool firstExists  = firstElementID >= 0;
                    const bool secondExists = secondElementID >= 0;

                    if (firstExists == secondExists) {
                        return false;
                    }

                    const int elementID = firstExists ? firstElementID : secondElementID;
                    const int domainID  = topology.element_domain_id(elementID);

                    return SchemaT::template domain_id_belongs_to<DomainT>(domainID);
                } else {
                    using FirstDomainT  = std::tuple_element_t<0, DomainsTuple>;
                    using SecondDomainT = std::tuple_element_t<1, DomainsTuple>;

                    if (firstElementID < 0 || secondElementID < 0) {
                        return false;
                    }

                    const int firstDomainID  = topology.element_domain_id(firstElementID);
                    const int secondDomainID = topology.element_domain_id(secondElementID);

                    const bool forwardMatch = SchemaT::template domain_id_belongs_to<FirstDomainT>(firstDomainID) &&
                                              SchemaT::template domain_id_belongs_to<SecondDomainT>(secondDomainID);

                    const bool reverseMatch = SchemaT::template domain_id_belongs_to<SecondDomainT>(firstDomainID) &&
                                              SchemaT::template domain_id_belongs_to<FirstDomainT>(secondDomainID);

                    return forwardMatch || reverseMatch;
                }
            };

            bool foundTaggedBoundary = false;

            // Forward validation: every boundary element carrying BoundaryT must
            // lie on exactly the interface declared by DomainBoundary.
            for (int boundaryElementID = 0; boundaryElementID < topology.boundary_element_count(); ++boundaryElementID) {
                const int boundaryID = topology.boundary_element_boundary_id(boundaryElementID);

                if (boundaryID != expectedBoundaryID) {
                    continue;
                }

                foundTaggedBoundary = true;

                const int faceID = topology.boundary_element_face(boundaryElementID);

                const auto [firstElementID, secondElementID] = topology.face_elements(faceID);

                if (!has_required_topology(firstElementID, secondElementID)) {
                    return {
                        .failure = RelationValidationFailure::DomainBoundaryTaggedFaceHasWrongTopology,
                        .domainBoundaryDiagnostics =
                            std::make_optional<RelationValidationResult::DomainBoundaryDiagnostics>(
                                make_diagnostics(faceID, boundaryElementID, boundaryID)
                            )
                    };
                }

                if (!face_matches_domains(firstElementID, secondElementID)) {
                    return {
                        .failure = RelationValidationFailure::DomainBoundaryTaggedFaceTouchesUnexpectedDomain,
                        .domainBoundaryDiagnostics =
                            std::make_optional<RelationValidationResult::DomainBoundaryDiagnostics>(
                                make_diagnostics(faceID, boundaryElementID, boundaryID)
                            )
                    };
                }
            }

            bool foundExpectedFace = false;

            // Reverse validation: every face having the declared domain
            // adjacency must carry BoundaryT.
            for (int faceID = 0; faceID < topology.face_count(); ++faceID) {
                const auto [firstElementID, secondElementID] = topology.face_elements(faceID);

                if (!face_matches_domains(firstElementID, secondElementID)) {
                    continue;
                }

                foundExpectedFace = true;

                const std::vector<int> &boundaryElementIDs = topology.boundary_elements_on_face(faceID);

                if (boundaryElementIDs.empty()) {
                    return {
                        .failure = RelationValidationFailure::DomainBoundaryExpectedFaceIsUntagged,
                        .domainBoundaryDiagnostics =
                            std::make_optional<RelationValidationResult::DomainBoundaryDiagnostics>(
                                make_diagnostics(faceID, -1, std::nullopt)
                            )
                    };
                }

                for (const int boundaryElementID : boundaryElementIDs) {
                    const int actualBoundaryID = topology.boundary_element_boundary_id(boundaryElementID);

                    if (actualBoundaryID == expectedBoundaryID) {
                        continue;
                    }

                    return {
                        .failure = RelationValidationFailure::DomainBoundaryExpectedFaceHasWrongID,
                        .domainBoundaryDiagnostics =
                            std::make_optional<RelationValidationResult::DomainBoundaryDiagnostics>(
                                make_diagnostics(faceID, boundaryElementID, actualBoundaryID)
                            )
                    };
                }
            }

            // If neither a correctly tagged boundary nor a face having the
            // required semantic topology exists, the declared DomainBoundary
            // simply is not realized by this mesh.
            if (!foundTaggedBoundary || !foundExpectedFace) {
                return {
                    .failure = RelationValidationFailure::DomainBoundaryAbsent,
                    .domainBoundaryDiagnostics =
                        std::make_optional<RelationValidationResult::DomainBoundaryDiagnostics>(
                            make_diagnostics(-1, -1, std::nullopt)
                        )
                };
            }

            return {};
        }
    };
}