/**
 * RegularGrid3D — Uniform 3D scalar/vector field for PDE solvers.
 *
 * Flat Float32Array storage with stencil operations (laplacian, gradient, divergence)
 * for finite difference methods. Shared by thermal, structural, and hydraulic solvers.
 */
export declare class RegularGrid3D {
    readonly nx: number;
    readonly ny: number;
    readonly nz: number;
    readonly components: number;
    readonly dx: number;
    readonly dy: number;
    readonly dz: number;
    readonly data: Float32Array;
    constructor(resolution: [number, number, number], domainSize: [number, number, number], components?: number);
    /** Flat index for cell (i, j, k) component c */
    private idx;
    get(i: number, j: number, k: number, component?: number): number;
    set(i: number, j: number, k: number, value: number, component?: number): void;
    /** Total number of cells */
    get cellCount(): number;
    /**
     * Discrete Laplacian ∇²f at (i,j,k) using 2nd-order central differences.
     *
     * BOUNDARY CONTRACT: This solver uses a flat array without ghost cells.
     * At boundaries (e.g. i=0 or i=nx-1), the partial derivative in that
     * direction is skipped. This results in a partial Laplacian which implicitly
     * enforces a homogeneous Neumann boundary condition (∂T/∂n = 0 / zero flux)
     * if no explicit boundary condition overwrites it after integration.
     */
    laplacian(i: number, j: number, k: number, component?: number): number;
    /**
     * Gradient ∇f at (i,j,k) using central differences.
     * Falls back to one-sided differences at boundaries.
     */
    gradient(i: number, j: number, k: number, component?: number): [number, number, number];
    /**
     * Divergence ∇·F for a 3-component vector field at (i,j,k).
     * Components 0,1,2 = x,y,z.
     */
    divergence(i: number, j: number, k: number): number;
    fill(value: number): void;
    copy(other: RegularGrid3D): void;
    /** this.data += scale * other.data (element-wise) */
    addScaled(other: RegularGrid3D, scale: number): void;
    /** L∞ norm (max absolute value) */
    maxAbs(): number;
    /** L2 norm */
    norm2(): number;
    /** Direct reference to the flat data buffer (for ScalarFieldOverlay) */
    toFloat32Array(): Float32Array;
    /**
     * Sample grid values at mesh vertex positions via trilinear interpolation.
     * @param positions Flat xyz vertex positions [x0,y0,z0, x1,y1,z1, ...]
     * @param domainOrigin World-space origin of the grid domain
     * @param component Which component to sample (default 0)
     */
    sampleAtPositions(positions: Float32Array, domainOrigin?: [number, number, number], component?: number): Float32Array;
    /**
     * Create a deep clone of this grid.
     */
    clone(): RegularGrid3D;
}
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